%AGagnon-Ririe, Levi%AYoung, Matthew%BJournal Name: Journal of Geometry and Physics; Journal Volume: 203; Journal Issue: C
%D2024%IElsevier
%JJournal Name: Journal of Geometry and Physics; Journal Volume: 203; Journal Issue: C
%KReal representation theory; Topological field theory; Frobenius algebras.
%MOSTI ID: 10525454
%PMedium: X
%TFrobeniusâ€“Schur indicators for twisted Real representation theory and two dimensional unoriented topological field theory
%XWe construct a two dimensional unoriented open/closed topological field theory from a finite graded group $\pi:\Gh \twoheadrightarrow \{1,-1\}$, a $\pi$-twisted $2$-cocycle $\hat{\theta}$ on $B \hat{G}$ and a character $\lambda: \hat{G} \rightarrow U(1)$. The underlying oriented theory is a twisted Dijkgraaf--Witten theory. The construction is based on a detailed study of the $(\hat{G}, \hat{\theta},\lambda)$-twisted Real representation theory of $\textnormal{ker} \pi$. In particular, twisted Real representations are boundary conditions of the unoriented theory and the generalized Frobenius--Schur element is its crosscap state.
%0Journal Article