arXiv 1506.080712015-06math.RT

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 Frez, José Pantoja

发表信息：: SIGMA 11 (2015), 076, 15 pages
DOI：: 10.3842/SIGMA.2015.076

英文摘要：

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

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