Lifting G(q)-modules

par Aura-Cristiana Radu (Newcastle )

jeudi 16 juin 2022, 11:15 → 12:15 Europe/Paris

112 (ICJ (Braconnier))

 

Lifting G(q)-modules (joint work with Dr David Stewart)

 

Let G be a simple, simply connected algebraic group over an algebraically closed field k of

characteristic p > 0. Then, for the r^th Frobenius map F^r : G → G, the fixed point set of

the points, G(q) := G(k)^{F^r}, is a finite group of Chevalley type. Let {L_1, . . . , L_m} be a list of not

necessarily distinct simple G-modules which are G(q)-simple on restriction. Then by L_1/L_2 . . . /L_m we denote the finite length composition series of a finite-length module M.

 

We explicitly determine the bounds on r such that G(q)-modules with an arbitrary number of composition factors lift to the ambient algebraic group G. That is, we determine

r_0(p, \Phi, m), so that for any r >=r_0, any G(q)-module M of the form L_1/ . . . /L_m is the restriction of a G-module M^{\tilde} of the form L_1/ . . . /L_m.