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
Issue number	1
Early online date	19 Dec 2018
DOIs	https://doi.org/10.1007/s10468-018-9843-z
Publication status	Published - Feb 2020

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

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10.1007/s10468-018-9843-zLicence: Unspecified

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

Cite this

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title = "Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic",

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.",

year = "2020",

month = feb,

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

language = "English",

volume = "23",

pages = "193--207",

journal = "Algebras and Representation Theory",

issn = "1386-923X",

publisher = "Springer Netherlands",

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TY - JOUR

T1 - Basic Sets for the Double Covering Groups of the Symmetric and Alternating Groups in Odd Characteristic

AU - Brunat, Olivier

AU - Gramain, Jean-Baptiste

N1 - 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.

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

KW - Basic set

KW - perfect isometries

KW - double covering groups of the symmetric and alternating groups

KW - modular representation theory

KW - Double covering groups of the symmetric and alternating groups

KW - Perfect isometries

KW - Modular representation theory

KW - REPRESENTATIONS

KW - BLOCKS

KW - BRAUER CHARACTERS

KW - FINITE-GROUPS

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U2 - 10.1007/s10468-018-9843-z

DO - 10.1007/s10468-018-9843-z

M3 - Article

VL - 23

SP - 193

EP - 207

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 1

ER -

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

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Jean-Baptiste Gramain

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

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Jean-Baptiste Gramain

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