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

DOI10.1016/J.LAA.2020.09.040arXiv2006.09765MaRDI QIDQ6343118

James Taylor, D. A. Rumynin

Publication date: 17 June 2020

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 $A_{n}leq{S}_n$.

Mathematics Subject Classification ID

Representation theory of groups (20C99) Twisted and skew group rings, crossed products (16S35)

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