Beijing Institute of Mathematical Sciences and Applications

Lin Zhe Huang , Zheng Wei Liu , Sébastien Palcoux , Yi Long Wang , Jin Song Wu

Mo Huang

Wednesday, May 8, 2024 10:30 AM - 12:00 PM

A3-3-301

Zoom 242 742 6089 (BIMSA)

The character plays an important role in the representation theory of finite groups. In this talk, I will introduce the notion of 2-character of 2-representations of a finite 2-group $\mathcal{G}$. The conjugation invariance implies that the 2-characters can be viewed as objects in the Drinfeld center ${\mathfrak{Z}}_1({\mathrm{Vec}}_{\mathcal{G}})$. I will also introduce a topological quantum field theory (TQFT) point of view on the 2-characters and show that they are Lagrangian algebras in ${\mathfrak{Z}}_1({\mathrm{Vec}}_{\mathcal{G}})$. Finally, I 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.