Higher Structures, Vol. 6, No. 1, pp. 359-374, 2022
Real Representations of $C_2$-Graded Groups: The Linear and Hermitian Theories
Dmitriy Rumynin, James Taylor
Received September 29th 2020. Published online July 15th 2022.
Abstract: We study linear and hermitian representations of finite $C_2$-graded groups. We prove that the category of linear representations is equivalent to a category of antilinear representations as an $\infty$-category. We also prove that the category of hermitian representations, as an $\infty$-category, is equivalent to a category of usual representations.
Keywords: Real representation; finite group; topological category; $\infty$-category
Affiliations: Dmitriy Rumynin, Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK, e-mail: d.rumynin@warwick.ac.uk; James Taylor, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK, e-mail: james.taylor@maths.ox.ac.uk
