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Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution
Інший ID:
2010 Mathematics Subject Classification: 20C33; 20C15; 20F05
DOI:10.3842/SIGMA.2015.076
DOI:10.3842/SIGMA.2015.076
Посилання:
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.
Підтримка:
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.
Дата:
2015
Переглядів:
464
Завантажень:
167
Анотація:
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.
