A Generalized Weil Representation for the Finite Split Orthogonal Group O-q (2n, 2n), q odd and > 3

作者：Vera Gajardo Andrea

来源：Journal of Lie Theory, 2015, 25(1): 257-270.

• Weil representation
• split orthogonal group
• involutive analogues of classical groups

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 (Sp(2)(F-q), 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).

• 出版日期2015