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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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| DOI | 10.3842/SIGMA.2015.076 | ||||
| Año | 2015 | ||||
| Tipo | artículo de investigación |
Citas Totales
Autores Afiliación Chile
Instituciones Chile
% Participación
Internacional
Autores
Afiliación Extranjera
Instituciones
Extranjeras
Abstract
We construct a complex linear Weil representation rho of the generalized special linear group G = SL*1(2, A(n)) =(A(n) = K[x]/< x(n)>, K the quadratic extension of the finite field k of q elements, q odd), where A(n) 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 rho.
| Ord. | Autor | Género | Institución - País |
|---|---|---|---|
| 1 | GUTIERREZ-FREZ, LUIS CRISTIAN | Hombre |
Universidad Austral de Chile - Chile
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| 2 | PANTOJA-MACARI, JOSE | Hombre |
Pontificia Universidad Católica de Valparaíso - Chile
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| Fuente |
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| FONDECYT |
| Universidad Austral de Chile |
| Pontificia Universidad Católica de Valparaíso |
| Agradecimiento |
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| 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 Catolica de Valparaiso. |
