The 2-character theory for finite 2-groups

by Hao Xu

Thursday 30 May 2024, 10:15 → 11:45 Europe/Zurich

Sitzungszimmer (MI)

Characters of finite groups play an important role in the representation theory. In this talk, I would like to introduce the categorification, that is the notion of 2-character for finite 2-groups. The conjugation invariance implies that 2-characters of G can be viewed as Lagrangian algebras in the Drinfeld center Z1(VectG). From a topological field theory point of view, 2-characters can be viewed as the value on the circle for some two dimensional G-TQFT. Lastly, we prove the orthognality of 2-characters. This is the joint work with Mo Huang and Zhi-Hao Zhang, arXiv:2404.01162.