Real Representations of $C_2$-Graded Groups: The Antilinear Theory
Representation Theory
2021-08-30 v4 Group Theory
Rings and Algebras
Abstract
We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite -graded groups. A finite -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 -graded group .
Keywords
Cite
@article{arxiv.2006.09765,
title = {Real Representations of $C_2$-Graded Groups: The Antilinear Theory},
author = {Dmitriy Rumynin and James Taylor},
journal= {arXiv preprint arXiv:2006.09765},
year = {2021}
}
Comments
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