
Journal of Lie Theory 25 (2015), No. 1, 257270 Copyright Heldermann Verlag 2015 A Generalized Weil Representation for the Finite Split Orthogonal Group O_{q}(2n,2n), q odd >3 Andrea Vera Gajardo P.A.I.E.P, Universidad de Santiago, Av. Libertador B. O'Higgins 3363, Santiago 9170022, Chile andreaveragajardo@gmail.com [Abstractpdf] \def\F{{\Bbb F}} We construct via generators and relations a generalized Weil representation for the split orthogonal group O$_q(2n,2n)$ 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 O$_q(2n,2n)$ for the reductive dual pair $({\rm Sp}_2(\F_q),{\rm O}_q(2n,2n))$ and that the initial decomposition is the same as the decomposition with respect to the action of Sp$_2(\F_q)$. Keywords: Weil representation, split orthogonal group, involutive analogues of classical groups. MSC: 20C33 [ Fulltextpdf (352 KB)] for subscribers only. 