Details
| Original language | English |
|---|---|
| Pages (from-to) | 778-814 |
| Number of pages | 37 |
| Journal | Representation theory |
| Volume | 27 |
| Early online date | 3 Nov 2023 |
| Publication status | Published - 2023 |
Abstract
For any finite group G and any prime p one can ask which ordinary irreducible representations remain irreducible in characteristic p, or more generally, which representations remain homogeneous in characteristic p. In this paper we address this question when G is a proper double cover of the symmetric or alternating group. We obtain a classification when p = 3 except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Representation theory, Vol. 27, 2023, p. 778-814.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the irreducible spin representations of symmetric and alternating groups which remain irreducible in characteristic 3
AU - Fayers, Matthew
AU - Morotti, Lucia
N1 - Funding Information: The first author was supported during this research by EPSRC Small Grant EP/W005751/1. This funding also allowed the second author to visit Queen Mary University of London, where some of this research was carried out. While working on the revised version the second author was working at Mathematisches Institut of the Heinrich-Heine-Universität Düsseldorf as well as the Department of Mathematics of the University of York. While working at the University of York the second author was supported by the Royal Society grant URF\R\221047.
PY - 2023
Y1 - 2023
N2 - For any finite group G and any prime p one can ask which ordinary irreducible representations remain irreducible in characteristic p, or more generally, which representations remain homogeneous in characteristic p. In this paper we address this question when G is a proper double cover of the symmetric or alternating group. We obtain a classification when p = 3 except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.
AB - For any finite group G and any prime p one can ask which ordinary irreducible representations remain irreducible in characteristic p, or more generally, which representations remain homogeneous in characteristic p. In this paper we address this question when G is a proper double cover of the symmetric or alternating group. We obtain a classification when p = 3 except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.
UR - http://www.scopus.com/inward/record.url?scp=85172199914&partnerID=8YFLogxK
U2 - 10.1090/ert/654
DO - 10.1090/ert/654
M3 - Article
AN - SCOPUS:85172199914
VL - 27
SP - 778
EP - 814
JO - Representation theory
JF - Representation theory
SN - 1088-4165
ER -