Cross characteristic representations of odd characteristic symplectic groups and unitary groups

Abstract

2016-12-26T15:09:09

The Ore conjecture

“…To do this, we consider the three unitary-Weil characters of H := Sp 2n (2) as described in [24]: α n of degree (2 n − 1)(2 n−1 − 1)/3, β n of degree (2 n + 1)(2 n−1 + 1)/3, and ζ 1 n of degree (2 2n − 1)/3.…”

Rational irreducible characters and rational conjugacy classes in finite groups

“…Observe that T * F * is isomorphic to Irr(T F ) (considered under multiplication), and the above correspondence Π specifies an isomorphism between them (cf. Remark 10.3 of [10]). Hence if (T , θ) corresponds to (T * , s) under Π, then the multiplicative order of θ is equal to n = o(s).…”

Character ratios for finite groups of Lie type, and applications

“…( [16]) Suppose G = Sp 2n (q) with q even and n ≥ 4. There is a collection W of q + 3 irreducible characters of G such that if 1 = χ ∈ Irr(G)\W, then…”

“…The characters in W are well understood: their degrees are all of the order of q 2n−1 , and information about their values is given in [16].…”