Cross characteristic representations of even characteristic symplectic groups

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

Lusztig’s conjecture for finite classical groups with even characteristic

The determination of scalars involved in Lusztig’s conjecture concerning the characters of finite reductive groups was achieved by Waldspurger in the case of finite classical groups Sp2n(Fq) or On(Fq) when p, q are large enough. Here p is the characteristic of the finite field Fq . In this paper, we determine the scalars in the case of Sp2n(Fq) with p = 2, by applying the theory of symmetric sp...

Characteristic Classes in Symplectic Topology

Characteristic Classes and Representations of Discrete Subgroups of Lie Groups

A volume invariant is used to characterize those representations of a countable group into a connected semisimple Lie group G which are injective and whose image is a discrete cocompact subgroup of G. Let IT be a discrete cocompact subgroup of G and consider the analytic variety Hom(7r, G) consisting of homomorphisms 0: TT —> G. Denote by K a maximal compact subgroup of G and X = K\G the associ...

On Representations of Algebraic Groups in Characteristic Two