Rumynin, Dmitriy and Taylor, James (2021) Real representations of C2-graded groups : the antilinear theory. Linear Algebra and Its Applications, 610 . pp. 135-168. doi:10.1016/j.laa.2020.09.040 ISSN 0024-3795.

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Abstract

We use the structure of finite-dimensional graded algebras to develop the theory of antilinear representations of finite C2-graded groups. A finite C2-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 C2-graded group An≤Sn.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Finite groups, Algebras, Linear, Blocking sets
Journal or Publication Title:	Linear Algebra and Its Applications
Publisher:	Elsevier Inc
ISSN:	0024-3795
Official Date:	1 February 2021
Dates:	Date Event 1 February 2021 Published 2 October 2020 Available 29 September 2020 Accepted
Volume:	610
Page Range:	pp. 135-168
DOI:	10.1016/j.laa.2020.09.040
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	7 October 2020
Date of first compliant Open Access:	2 October 2021

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