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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications // Archive

SIGMA, 2015 Volume 11, 076, 15 pp. (Mi sigma1057)

This article is cited in 1 paper

Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution

Luis Gutiérrez Freza, José Pantojab

a Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Campus Isla Teja SN, Edificio Pugín, Valdivia, Chile
b Instituto de Matemáticas, Pontificia Universidad Catolica de Valparaíso, Blanco Viel 596, Co. Barón, Valparaíso, Chile

Abstract: We construct a complex linear Weil representation $\rho$ of the generalized special linear group $G=\mathrm{SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\langle x^n\rangle $, $K$ 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 $\rho$.

Keywords: Weil representation; generalized special linear group.

MSC: 20C33; 20C15; 20F05

Received: July 3, 2015; in final form September 14, 2015; Published online September 26, 2015

Language: English

DOI: 10.3842/SIGMA.2015.076



Bibliographic databases:
ArXiv: 1506.08071


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