2-Character Theory of Finite 2-Groups

Learn about the 2-character theory of finite 2-groups in this academic seminar talk from the BIMSA-Tsinghua Quantum Symmetry Series. Explore how characters function in the representation theory of finite groups, with a focus on 2-characters of 2-representations of finite 2-group $\mathcal{G}$. Examine conjugation invariance and how 2-characters relate to the Drinfeld center $\mathfrak{Z}_1(\mathrm{Vec}_{\mathcal{G}})$. Discover the topological quantum field theory (TQFT) perspective on 2-characters and their role as Lagrangian algebras. Delve into the orthogonality of 2-characters and their relationship to classical character orthogonality. Based on collaborative research presented by Mo Huang from East China Normal University, this talk references works from arXiv: 2305.18151 and 2404.01162, developed jointly with Hao Xu and Zhi-Hao Zhang.