On generalized decomposition numbers and Fong's reductions
type: Item
instance of: scholarly article
title: On generalized decomposition numbers and Fong's reductions
zbMATH Open document ID: 0575.20011
author: Atumi Watanabe
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Fong's reduction theorems relate blocks of a group G to blocks of some subgroup or some factor group of G. They have proved to be an important tool in representation theory of (mainly p-solvable) groups. Among the properties invariant under these reductions are the numbers of ordinary and modular irreducible characters, the Cartan and decomposition matrices. Here the author investigates the behaviour of generalized decomposition numbers. In the first reduction, generalized decomposition numbers remain invariant, whereas in the second reduction generalized decomposition numbers are invariant up to a sign, the sign coming from an application of the Glauberman correspondence for characters.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C11
zbMATH DE Number: 3918636
zbMATH Keywords: Fong's reduction theorems
zbMATH Keywords: blocks
zbMATH Keywords: numbers of ordinary and modular irreducible characters
zbMATH Keywords: decomposition matrices
zbMATH Keywords: generalized decomposition numbers
zbMATH Keywords: Glauberman correspondence
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3918636