Representation and character theory in 2-categories

TL;DR

This paper extends the concept of group representation characters to 2-categories, establishing a new character theory framework that generalizes classical notions and includes explicit formulas for induced representations.

Contribution

It introduces a novel character theory for group representations in 2-categories, generalizing classical character theory to higher categorical contexts.

Findings

Defined the character of a group representation in a 2-category

Established a Hopkins-Kuhn-Ravenel type character theory for linear 2-categories

Proved a formula for the character of induced representations

Abstract

We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a formula for the character of the induced representation.