Journal of Lie Theory

no. 1
A Generalized Weil Representation for the Finite Split Orthogonal Group Oq(2n,2n), q odd >3
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 257-270
\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$_2(\F_q)$.
DOI: 10.5802/jolt.836
Classification: 20C33
Keywords: Weil representation, split orthogonal group, involutive analogues of classical groups 
@article{JOLT_2015_25_1_a12,
     author = {A. Vera Gajardo},
     title = {A {Generalized} {Weil} {Representation} for the {Finite} {Split} {Orthogonal} {Group} {O\protect\textsubscript{q}(2n,2n),} q odd >3},
     journal = {Journal of Lie Theory},
     pages = {257--270},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.836},
     zbl = {1316.20048},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.836/}
}
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%A A. Vera Gajardo
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%J Journal of Lie Theory
%D 2015
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A. Vera Gajardo. A Generalized Weil Representation for the Finite Split Orthogonal Group Oq(2n,2n), q odd >3. Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 257-270. doi: 10.5802/jolt.836

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