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arXiv · 2006.09765

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

Dmitriy Rumynin·James Taylor
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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 $A_n \leq S_n$.

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BibTeXRIS

Dmitriy Rumynin, James Taylor. 2020-06-17. Real Representations of $C_2$-Graded Groups: The Antilinear Theory. https://doi.org/10.1016/j.laa.2020.09.040

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