Extending Snow’s algorithm for computations in the finite Weyl groups
Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse el...
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| Autor*in: |
Stekolshchik, Rafael [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Anmerkung: |
© The Author(s) 2023 |
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| Übergeordnetes Werk: |
Enthalten in: Fixed point theory and applications - Heidelberg : Springer, 2004, 2023(2023), 1 vom: 20. Nov. |
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| Übergeordnetes Werk: |
volume:2023 ; year:2023 ; number:1 ; day:20 ; month:11 |
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10.1186/s13663-023-00755-w |
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| 520 | |a Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. | ||
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10.1186/s13663-023-00755-w doi (DE-627)SPR053790529 (SPR)s13663-023-00755-w-e DE-627 ger DE-627 rakwb eng Stekolshchik, Rafael verfasserin aut Extending Snow’s algorithm for computations in the finite Weyl groups 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2023(2023), 1 vom: 20. Nov. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2023 year:2023 number:1 day:20 month:11 https://dx.doi.org/10.1186/s13663-023-00755-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2023 2023 1 20 11 |
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10.1186/s13663-023-00755-w doi (DE-627)SPR053790529 (SPR)s13663-023-00755-w-e DE-627 ger DE-627 rakwb eng Stekolshchik, Rafael verfasserin aut Extending Snow’s algorithm for computations in the finite Weyl groups 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2023(2023), 1 vom: 20. Nov. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2023 year:2023 number:1 day:20 month:11 https://dx.doi.org/10.1186/s13663-023-00755-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2023 2023 1 20 11 |
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10.1186/s13663-023-00755-w doi (DE-627)SPR053790529 (SPR)s13663-023-00755-w-e DE-627 ger DE-627 rakwb eng Stekolshchik, Rafael verfasserin aut Extending Snow’s algorithm for computations in the finite Weyl groups 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2023(2023), 1 vom: 20. Nov. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2023 year:2023 number:1 day:20 month:11 https://dx.doi.org/10.1186/s13663-023-00755-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2023 2023 1 20 11 |
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10.1186/s13663-023-00755-w doi (DE-627)SPR053790529 (SPR)s13663-023-00755-w-e DE-627 ger DE-627 rakwb eng Stekolshchik, Rafael verfasserin aut Extending Snow’s algorithm for computations in the finite Weyl groups 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2023(2023), 1 vom: 20. Nov. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2023 year:2023 number:1 day:20 month:11 https://dx.doi.org/10.1186/s13663-023-00755-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2023 2023 1 20 11 |
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10.1186/s13663-023-00755-w doi (DE-627)SPR053790529 (SPR)s13663-023-00755-w-e DE-627 ger DE-627 rakwb eng Stekolshchik, Rafael verfasserin aut Extending Snow’s algorithm for computations in the finite Weyl groups 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2023(2023), 1 vom: 20. Nov. (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2023 year:2023 number:1 day:20 month:11 https://dx.doi.org/10.1186/s13663-023-00755-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 2023 2023 1 20 11 |
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extending snow’s algorithm for computations in the finite weyl groups |
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Extending Snow’s algorithm for computations in the finite Weyl groups |
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Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. © The Author(s) 2023 |
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Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. © The Author(s) 2023 |
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Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python. © The Author(s) 2023 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR053790529</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231120064808.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231120s2023 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1186/s13663-023-00755-w</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR053790529</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13663-023-00755-w-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stekolshchik, Rafael</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Extending Snow’s algorithm for computations in the finite Weyl groups</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2023</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$: with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python.</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Fixed point theory and applications</subfield><subfield code="d">Heidelberg : Springer, 2004</subfield><subfield code="g">2023(2023), 1 vom: 20. Nov.</subfield><subfield code="w">(DE-627)379482037</subfield><subfield code="w">(DE-600)2135860-6</subfield><subfield code="x">1687-1812</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:2023</subfield><subfield code="g">year:2023</subfield><subfield code="g">number:1</subfield><subfield code="g">day:20</subfield><subfield code="g">month:11</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1186/s13663-023-00755-w</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">2023</subfield><subfield code="j">2023</subfield><subfield code="e">1</subfield><subfield code="b">20</subfield><subfield code="c">11</subfield></datafield></record></collection>
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