Frobenius--Schur indicators for twisted Real representation theory and two dimensional unoriented topological field theory

2023/10/05 by Gagnon-Ririe, Levi, Young, Matthew B.
#FOS: Mathematics #Primary: 20C25 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 81T45

paper · doi:10.48550/arxiv.2310.03566

Abstract

We construct a two dimensional unoriented open/closed topological field theory from a finite graded group π:G \twoheadrightarrow \1,-1\, a π-twisted 2-cocycle θ on B G and a character λ: G → U(1). The underlying oriented theory is a twisted Dijkgraaf-Witten theory. The construction is based in the (G, θ,λ)-twisted Real representation theory of ker π. In particular, twisted Real representations are boundary conditions and the generalized Frobenius-Schur element is its crosscap state.

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