Mathematics Colloquium
Date: Wednesday, 18 October 2023
Time: 3:30 - 4:30 PM
Venue: Seminar Hall
Stiefel-Whitney Classes for Representations of Finite Symplectic Groups
Neha Malik
Chennai Mathematical Institute.
18-10-23

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Abstract

Orthogonal representations $\pi$ of a finite group $G$ have cohomological invariants $w_i(\pi)$ living in the $i$th degree cohomology group $H^i(G,Z/2Z)$, called Stiefel-Whitney Classes (SWCs).

There are not many explicit calculations in the literature on characteristic classes for the non-abelian groups. We have computed SWCs for several finite groups of Lie type in terms of character values at diagonal involutions. This talk will begin with a brief introduction to these classes, followed by an overview of our results for finite symplectic groups $Sp(2n,q)$ when $q$ is odd. We will also discuss a Nakaoka-type result which, in a sense, conveys that the cohomology of $Sp(2n,q)$ stabilizes.