Modular Representations and Indicators for Bismash Products

TL;DR

This paper develops Brauer characters for bismash product representations in characteristic p and extends a classical theorem on Frobenius-Schur indicators to these structures.

Contribution

It introduces Brauer characters for bismash products and generalizes Thompson's theorem on lifting indicators from characteristic p to 0.

Findings

Brauer characters for bismash products are constructed and analyzed.

Properties of these characters mirror classical finite group cases.

Thompson's theorem on indicator lifting is extended to bismash products.

Abstract

We introduce Brauer characters for representations of the bismash products of groups in characteristic p > 0, p not 2 and study their properties analogous to the classical case of finite groups. We then use our results to extend to bismash products a theorem of Thompson on lifting Frobenius-Schur indicators from characteristic p to characteristic 0