Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic

Olivier Brunat; Jean-Baptiste Gramain

doi:10.1007/s10468-018-9843-z

Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic

Olivier Brunat (Corresponding Author), Jean-Baptiste Gramain

Mathematical Science

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Abstract

In this paper, following the methods of Brunat and Gramain (J. Reine Angew. Math. 641, 5 177–202, 2010), we show that the double covering groups of the symmetric and alternating 6 groups have p-basic sets for any odd prime p.

Original language	English
Pages (from-to)	193-207
Number of pages	15
Journal	Algebras and Representation Theory
Volume	23
Early online date	19 Dec 2018
DOIs	https://doi.org/10.1007/s10468-018-9843-z
Publication status	Published - Feb 2020

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Keywords

Basic set
perfect isometries
double covering groups of the symmetric and alternating groups
modular representation theory
Double covering groups of the symmetric and alternating groups
Perfect isometries
Modular representation theory
REPRESENTATIONS
BLOCKS
BRAUER CHARACTERS
FINITE-GROUPS

ASJC Scopus subject areas

Mathematics(all)

Cite this

Brunat, O., & Gramain, J-B. (2020). Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic. Algebras and Representation Theory, 23, 193-207. https://doi.org/10.1007/s10468-018-9843-z

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abstract = "In this paper, following the methods of Brunat and Gramain (J. Reine Angew. Math. 641, 5 177–202, 2010), we show that the double covering groups of the symmetric and alternating 6 groups have p-basic sets for any odd prime p.",

keywords = "Basic set, perfect isometries, double covering groups of the symmetric and alternating groups, modular representation theory, Double covering groups of the symmetric and alternating groups, Perfect isometries, Modular representation theory, REPRESENTATIONS, BLOCKS, BRAUER CHARACTERS, FINITE-GROUPS",

author = "Olivier Brunat and Jean-Baptiste Gramain",

note = "Acknowledgements. Part of this work was done at the CIRM in Luminy during a research in pairs stay. The authors wish to thank the CIRM gratefully for their financial and logistical support. The first author is supported by Agence Nationale de la Recherche Projet ACORT ANR-12-JS01-0003. The second author also acknowledges financial support from the Engineering and Physical Sciences Research Council grant Combinatorial Representation Theory EP/M019292/1. The authors wish to thank the referee for several helpful suggestions.",

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doi = "10.1007/s10468-018-9843-z",

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KW - modular representation theory

KW - Double covering groups of the symmetric and alternating groups

KW - Perfect isometries

KW - Modular representation theory

KW - REPRESENTATIONS

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Accepted Manuscript
This is a post-peer-review, pre-copyedit version of an article published in Algebras and Representation Theory. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10468-018-9843-z
Accepted author manuscript, 511 KBLicence: Unspecified

http://arxiv.org/abs/1606.02631v1Licence: Unspecified
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