An equivariant rim hook rule for quantum cohomology of Grassmannians

A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schuber...
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Gespeichert in:

Autor*in:	Elizabeth Beazley [verfasserIn] Anna Bertiger [verfasserIn] Kaisa Taipale [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co]

Übergeordnetes Werk:	In: Discrete Mathematics & Theoretical Computer Science - Discrete Mathematics & Theoretical Computer Science, 2004, (2014), Proceedings
Übergeordnetes Werk:	year:2014 ; number:Proceedings

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.46298/dmtcs.2377

Katalog-ID:	DOAJ097147850

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allfields	10.46298/dmtcs.2377 doi (DE-627)DOAJ097147850 (DE-599)DOAJe6cba77969844010a17a302118d750b1 DE-627 ger DE-627 rakwb eng QA1-939 Elizabeth Beazley verfasserin aut An equivariant rim hook rule for quantum cohomology of Grassmannians 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus. schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics Anna Bertiger verfasserin aut Kaisa Taipale verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2014), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2014 number:Proceedings https://doi.org/10.46298/dmtcs.2377 kostenfrei https://doaj.org/article/e6cba77969844010a17a302118d750b1 kostenfrei https://dmtcs.episciences.org/2377/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2014 Proceedings
spelling	10.46298/dmtcs.2377 doi (DE-627)DOAJ097147850 (DE-599)DOAJe6cba77969844010a17a302118d750b1 DE-627 ger DE-627 rakwb eng QA1-939 Elizabeth Beazley verfasserin aut An equivariant rim hook rule for quantum cohomology of Grassmannians 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus. schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics Anna Bertiger verfasserin aut Kaisa Taipale verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2014), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2014 number:Proceedings https://doi.org/10.46298/dmtcs.2377 kostenfrei https://doaj.org/article/e6cba77969844010a17a302118d750b1 kostenfrei https://dmtcs.episciences.org/2377/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2014 Proceedings
allfields_unstemmed	10.46298/dmtcs.2377 doi (DE-627)DOAJ097147850 (DE-599)DOAJe6cba77969844010a17a302118d750b1 DE-627 ger DE-627 rakwb eng QA1-939 Elizabeth Beazley verfasserin aut An equivariant rim hook rule for quantum cohomology of Grassmannians 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus. schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics Anna Bertiger verfasserin aut Kaisa Taipale verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2014), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2014 number:Proceedings https://doi.org/10.46298/dmtcs.2377 kostenfrei https://doaj.org/article/e6cba77969844010a17a302118d750b1 kostenfrei https://dmtcs.episciences.org/2377/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2014 Proceedings
allfieldsGer	10.46298/dmtcs.2377 doi (DE-627)DOAJ097147850 (DE-599)DOAJe6cba77969844010a17a302118d750b1 DE-627 ger DE-627 rakwb eng QA1-939 Elizabeth Beazley verfasserin aut An equivariant rim hook rule for quantum cohomology of Grassmannians 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus. schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics Anna Bertiger verfasserin aut Kaisa Taipale verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2014), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2014 number:Proceedings https://doi.org/10.46298/dmtcs.2377 kostenfrei https://doaj.org/article/e6cba77969844010a17a302118d750b1 kostenfrei https://dmtcs.episciences.org/2377/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2014 Proceedings
allfieldsSound	10.46298/dmtcs.2377 doi (DE-627)DOAJ097147850 (DE-599)DOAJe6cba77969844010a17a302118d750b1 DE-627 ger DE-627 rakwb eng QA1-939 Elizabeth Beazley verfasserin aut An equivariant rim hook rule for quantum cohomology of Grassmannians 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus. schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics Anna Bertiger verfasserin aut Kaisa Taipale verfasserin aut In Discrete Mathematics & Theoretical Computer Science Discrete Mathematics & Theoretical Computer Science, 2004 (2014), Proceedings (DE-627)239019105 (DE-600)1412155-4 13658050 nnns year:2014 number:Proceedings https://doi.org/10.46298/dmtcs.2377 kostenfrei https://doaj.org/article/e6cba77969844010a17a302118d750b1 kostenfrei https://dmtcs.episciences.org/2377/pdf kostenfrei https://doaj.org/toc/1365-8050 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2119 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2014 Proceedings
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topic_facet	schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] Mathematics
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callnumber-first	Q - Science
author	Elizabeth Beazley
spellingShingle	Elizabeth Beazley misc QA1-939 misc schubert calculus misc quantum equivariant cohomology misc rim hook misc abacus diagram misc factorial schur function misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc [math.math-co] mathematics [math]/combinatorics [math.co] misc Mathematics An equivariant rim hook rule for quantum cohomology of Grassmannians
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topic_title	QA1-939 An equivariant rim hook rule for quantum cohomology of Grassmannians schubert calculus quantum equivariant cohomology rim hook abacus diagram factorial schur function [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co]
topic	misc QA1-939 misc schubert calculus misc quantum equivariant cohomology misc rim hook misc abacus diagram misc factorial schur function misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc [math.math-co] mathematics [math]/combinatorics [math.co] misc Mathematics
topic_unstemmed	misc QA1-939 misc schubert calculus misc quantum equivariant cohomology misc rim hook misc abacus diagram misc factorial schur function misc [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] misc [math.math-co] mathematics [math]/combinatorics [math.co] misc Mathematics
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title	An equivariant rim hook rule for quantum cohomology of Grassmannians
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title_full	An equivariant rim hook rule for quantum cohomology of Grassmannians
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title_sort	equivariant rim hook rule for quantum cohomology of grassmannians
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title_auth	An equivariant rim hook rule for quantum cohomology of Grassmannians
abstract	A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus.
abstractGer	A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus.
abstract_unstemmed	A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis. Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. Interestingly, this rule requires a specialization of torus weights that is tantalizingly similar to maps in affine Schubert calculus.
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container_issue	Proceedings
title_short	An equivariant rim hook rule for quantum cohomology of Grassmannians
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Bertram, Ciocan-Fontanine and Fulton provide a way to compute quantum products of Schubert classes in the Grassmannian of $k$-planes in complex $n$-space by doing classical multiplication and then applying a combinatorial rimhook rule which yields the quantum parameter. In this paper, we provide a generalization of this rim hook rule to the setting in which there is also an action of the complex torus. Combining this result with Knutson and Tao's puzzle rule provides an effective algorithm for computing the equivariant quantum Littlewood-Richardson coefficients. 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code="a">Mathematics</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">Anna Bertiger</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="0" ind2=" "><subfield code="a">Kaisa Taipale</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Discrete Mathematics & Theoretical Computer Science</subfield><subfield code="d">Discrete Mathematics & Theoretical Computer Science, 2004</subfield><subfield code="g">(2014), Proceedings</subfield><subfield code="w">(DE-627)239019105</subfield><subfield code="w">(DE-600)1412155-4</subfield><subfield code="x">13658050</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">year:2014</subfield><subfield code="g">number:Proceedings</subfield></datafield><datafield 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An equivariant rim hook rule for quantum cohomology of Grassmannians

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