The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types

Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^*_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an id...
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Autor*in:	Harada, Megumi [verfasserIn] Horiguchi, Tatsuya Masuda, Mikiya

Format:	Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Secondary: 14N15 Primary: 55N91 Algebraic Geometry Algebraic Topology Mathematics

Übergeordnetes Werk:	Enthalten in: Canadian mathematical bulletin - Toronto : Univ. of Toronto Press, 1958, 58(2015), 1, Seite 80-90
Übergeordnetes Werk:	volume:58 ; year:2015 ; number:1 ; pages:80-90

Links:	Volltext Link aufrufen

DOI / URN:	10.4153/CMB-2014-048-0

Katalog-ID:	OLC1963934474

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520			\|a Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group S \cong \mathbb{C}^ is a certain subgroup of a maximal torus T of G. Our description of the ideal J uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type A.
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spelling	10.4153/CMB-2014-048-0 doi PQ20160617 (DE-627)OLC1963934474 (DE-599)GBVOLC1963934474 (PRQ)a1360-724986126cb26b63484b44e7e3e84930d82e782e515e5d724b10df1041e062620 (KEY)0023676420150000058000100080equivariantcohomologyringsofpetersonvarietiesinall DE-627 ger DE-627 rakwb eng 510 DNB 31.00 bkl Harada, Megumi verfasserin aut The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group S \cong \mathbb{C}^ is a certain subgroup of a maximal torus T of G. Our description of the ideal J uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type A. Secondary: 14N15 Primary: 55N91 Algebraic Geometry Algebraic Topology Mathematics Horiguchi, Tatsuya oth Masuda, Mikiya oth Enthalten in Canadian mathematical bulletin Toronto : Univ. of Toronto Press, 1958 58(2015), 1, Seite 80-90 (DE-627)129852163 (DE-600)280584-4 (DE-576)01515226X 0008-4395 nnns volume:58 year:2015 number:1 pages:80-90 http://dx.doi.org/10.4153/CMB-2014-048-0 Volltext http://arxiv.org/abs/1405.1785 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_24 GBV_ILN_30 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_4036 GBV_ILN_4126 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4324 31.00 AVZ AR 58 2015 1 80-90
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topic_title	510 DNB 31.00 bkl The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types Secondary: 14N15 Primary: 55N91 Algebraic Geometry Algebraic Topology Mathematics
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title	The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
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title_full	The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
author_sort	Harada, Megumi
journal	Canadian mathematical bulletin
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author-letter	Harada, Megumi
doi_str_mv	10.4153/CMB-2014-048-0
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title_sort	equivariant cohomology rings of peterson varieties in all lie types
title_auth	The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
abstract	Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group S \cong \mathbb{C}^ is a certain subgroup of a maximal torus T of G. Our description of the ideal J uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type A.
abstractGer	Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group S \cong \mathbb{C}^ is a certain subgroup of a maximal torus T of G. Our description of the ideal J uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type A.
abstract_unstemmed	Let G be a complex semisimple linear algebraic group and let Pet be the associated Peterson variety in the flag variety G/B. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring H^_S(Pet) of the Peterson variety as a quotient of a polynomial ring by an ideal J generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group S \cong \mathbb{C}^ is a certain subgroup of a maximal torus T of G. Our description of the ideal J uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type A.
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container_issue	1
title_short	The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
url	http://dx.doi.org/10.4153/CMB-2014-048-0 http://arxiv.org/abs/1405.1785
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author2	Horiguchi, Tatsuya Masuda, Mikiya
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up_date	2024-07-04T06:50:11.388Z
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