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arXiv · 1311.1174

A Generalized Weil Representation for the finite split orthogonal group $O_q(2n,2n)$, $q$ odd greater than $3$

Andrea Vera Gajardo
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Abstract

We construct via generators and relations a generalized Weil representation for the split orthogonal group $\ot_q(2n,2n)$ over a finite field of $q$ elements. Besides, we give an initial decomposition of the representation found. We also show that the constructed representation is equal to the restriction of the Weil representation to $\ot_q(2n,2n)$ for the reductive dual pair $(\Sp_2(\mathbb{F}_q),\ot_q(2n,2n))$ and that the initial decomposition is the same as the decomposition with respect to the action of $\Sp_2(\mathbb{F}_q)$.

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BibTeXRIS

Andrea Vera Gajardo. 2014-06-25. A Generalized Weil Representation for the finite split orthogonal group $O_q(2n,2n)$, $q$ odd greater than $3$. https://arxiv.org/abs/1311.1174

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