The Weil-Steinberg character of finite classical groups

Hiss, G.; Zalesski, A.

doi:10.1090/S1088-4165-09-00351-3

The Weil-Steinberg character of finite classical groups
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by G. Hiss and A. Zalesski; \\ with an appendix by Olivier Brunat PDF

Represent. Theory 13 (2009), 427-459 Request permission

Corrigendum: Represent. Theory 15 (2011), 729-732.

Abstract:

Let $G$ be one of the groups $\operatorname {GL}(n,q)$ or $U(n,q)$, and let $H$ denote the subgroup $\operatorname {GL}({n-1},q)$ or $U(n-1,q)$, respectively. We show that the restriction of the Steinberg character of $G$ to $H$ equals the product of the Weil character and the Steinberg character of $H$.

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