Lusztig's conjecture for finite classical groups with even characteristic

Details Lusztig's conjecture for finite classical groups with even characteristic Lusztig's conjecture for finite classical groups with even characteristic

2007-12-14

arxiv.org/abs/0712.2296v1

Mathematics

Representation Theory

30 pages

Scientific paper

The determination of scalars involved in Lusztig's conjecture for finite reductive groups $G(F_q)$ was achieved by Waldspurger in the case of symplectic groups or orthogonal groups, under the condition that $p,q$ are large enough. Here $p$ is the characteristic of the finite field $F_q$. In this paper, we determine the scalars in the case of symplectic groups with $p = 2$, by applying the theory of symmetric spaces over a finite field due to Kawanaka and Lusztig. We also obtain a partial result in the case of special orthogonal groups with $p = 2$.

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