WEIL REPRESENTATIONS OF FINITE GENERAL LINEAR GROUPS AND FINITE SPECIAL LINEAR GROUPS

摘要

Let q be a prime power and let G(n) be the general linear group GL(n) (q) the special linear group SLn (q), with n >= 4. We prove two characterization theorems for the Weil representations of G(n) in any characteristic coprime to q, one in terms of the restriction to a standard subgroup G(n-1), and another in terms of the restriction to a maximal parabolic subgroup of G(n).