Abstract

The character plays an important role in the representation theory of finite groups. in this talk, lwill introduce the notion of 2-character of 2-representations of a finite 2-group G. The conjugationinvariance implies that the 2-characters can be viewed as objects in the Drinfeld center 31(Vecg).will also introduce a topological guantum field theory (TQFT) point of view on the 2-characters andshow that they are Lagrangian algebras in 3,(Vecg). Finally, l will discuss the orthogonality of 2-characters, which categorifies the classical orthogonality of characters. This talk is based on arXiv.2305.18151 and 2404.01162, joint with Hao Xu and Zhi-Hao Zhang.