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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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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irk-123456789-1471102019-02-14T01:23:48Z 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. 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. 2015 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147110 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Gutiérrez Frez, L. Pantoja, J. |
| spellingShingle |
Gutiérrez Frez, L. Pantoja, J. Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gutiérrez Frez, L. Pantoja, J. |
| author_sort |
Gutiérrez Frez, L. |
| 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_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_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_sort |
weil representation of a generalized linear group over a ring of truncated polynomials over a finite field endowed with a second class involution |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147110 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
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2025-07-11T01:23:10Z |
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2025-07-11T01:23:10Z |
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