Mathematical-Physical Colloquium in Summer Semester 2022

We would like to invite you to the Mathematical-Physical Colloquium of the Faculty of Mathematics and Physics at Leibniz Universität Hannover:

Dr. Lucia Morotti (Leibniz Universität Hannover)

speaks on the topic

Homogeneous reductions of spin representations

in Room B302 on Tuesday, 3 May 2022 at 16:30.

This is her inaugural lecture as part of the habilitation process.

Abstract: Let V be a representation of a finite group G defined over a field k of characteristic 0. Up to possibly extending k, it is possible to find a subring R of k such that the R-span of a k-basis of V is G-stable. Coefficients can be then reduced modulo any maximal ideal of R to obtain a new representation V'. If the new field has characteristic p we say that V' is the reduction modulo p of V.

In general V' is not irreducible, even if V was. We say that V' is homogeneous if all of its composition factors are isomorphic. Clearly V' is homogeneous if it is irreducible, but the reverse does not necesearily hold.

A natural question can be, given a group G and a prime p, to classify all irreducible representations of G which are irreducible or homogeneous when reduced modulo p.

In this talk I will consider this question in the case where G is a double cover of a symmetric group and p=3. This is joint work with Matthew Fayers.