Real Representations of $C_2$-Graded Groups: The Antilinear Theory

Abstract

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite $C_2$-graded groups. A finite $C_2$-graded group is a finite group with a subgroup of index 2. In this theory the subgroup acts linearly, while the other coset acts antilinearly. We introduce antilinear blocks, whose structure is a crucial component of the theory. Among other things, we study characters and Frobenius-Schur indicators. As an example, we describe the antilinear representations of the $C_2$-graded group $A_n\le S_n$.

Version 2: typos are corrected, reference to Dyson and explanation of Dyson's work are added. Version 3: minor corrections, final published version. Version 4: a post publication appendix with two typos corrected

References in corpus (1)

• Twisted loop transgression and higher Jandl gerbes over finite groupoids

Cited by in corpus (1)

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