A basic set for the alternating group

Olivier Brunat, Jean-Baptiste Gramain

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This article is concerned with the p-basic set existence problem in the representation theory of finite groups. We show that, for any odd prime p, the alternating group 프n has a p-basic set. More precisely, we prove that the symmetric group 픖n has a p-basic set with some additional properties, allowing us to deduce a p-basic set for 프n. Our main tool is the concept of generalized perfect isometries introduced by Külshammer, Olsson and Robinson. As a consequence we obtain some results on the decomposition numbers of 프n.
Original languageEnglish
Pages (from-to)177-202
Number of pages26
JournalJournal für die reine und angewandte Mathematik
Volume641
DOIs
Publication statusPublished - Jan 2010

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