Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution
We construct a complex linear Weil representation ρ of the generalized special linear group G=SL¹∗(2,An) (An=K[x]/⟨xⁿ⟩, K the quadratic extension of the finite field k of q elements, q odd), where An is endowed with a second class involution. After the construction of a specific data, the representa...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147110 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution / L. Gutiérrez Frez, J. Pantoja // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862657252338434048 |
|---|---|
| author | Gutiérrez Frez, L. Pantoja, J. |
| author_facet | Gutiérrez Frez, L. Pantoja, J. |
| citation_txt | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution / L. Gutiérrez Frez, J. Pantoja // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We construct a complex linear Weil representation ρ of the generalized special linear group G=SL¹∗(2,An) (An=K[x]/⟨xⁿ⟩, K the quadratic extension of the finite field k of q elements, q odd), where An is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of G, via linear operators satisfying the relations of the presentation. The structure of a unitary group U associated to G is described. Using this group we obtain a first decomposition of ρ.
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| first_indexed | 2025-12-02T05:40:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147110 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T05:40:53Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gutiérrez Frez, L. Pantoja, J. 2019-02-13T16:50:23Z 2019-02-13T16:50:23Z 2015 Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution / L. Gutiérrez Frez, J. Pantoja // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C33; 20C15; 20F05 DOI:10.3842/SIGMA.2015.076 https://nasplib.isofts.kiev.ua/handle/123456789/147110 We construct a complex linear Weil representation ρ of the generalized special linear group G=SL¹∗(2,An) (An=K[x]/⟨xⁿ⟩, K the quadratic extension of the finite field k of q elements, q odd), where An is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of G, via linear operators satisfying the relations of the presentation. The structure of a unitary group U associated to G is described. Using this group we obtain a first decomposition of ρ. We thank Pierre Cartier for his comments and suggestions at the beginning of this work. Both
 authors were partially supported by FONDECYT grant 1120578. Moreover, the first author
 was partially supported by the Universidad Austral de Chile, while the second author was also
 partially supported by Pontificia Universidad Cat´olica de Valpara´ıso. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution Article published earlier |
| spellingShingle | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution Gutiérrez Frez, L. Pantoja, J. |
| title | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution |
| title_full | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution |
| title_fullStr | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution |
| title_full_unstemmed | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution |
| title_short | Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution |
| title_sort | weil representation of a generalized linear group over a ring of truncated polynomials over a finite field endowed with a second class involution |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147110 |
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