Perfect Isometries and Murnaghan-Nakayama Rules

Olivier Brunat, Jean-Baptiste Gramain

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Abstract

This article is concerned with perfect isometries between blocks
of finite groups. Generalizing a method of Enguehard to show that any two
p-blocks of (possibly different) symmetric groups with the same weight are
perfectly isometric, we prove analogues of this result for p-blocks of alternating
groups (where the blocks must also have the same sign when p is odd), of
double covers of alternating and symmetric groups (for p odd, and where we
obtain crossover isometries when the blocks have opposite signs), of complex
reflection groups G(d, 1, n) (for d prime to p), of Weyl groups of type B and
D (for p odd), and of certain wreath products. In order to do this, we need
to generalize the theory of blocks in a way which should be of independent
interest.
Original languageEnglish
Pages (from-to)7657-7718
Number of pages62
JournalTransactions of the American Mathematical Society
Volume369
Issue number11
Early online date11 May 2017
DOIs
Publication statusPublished - 2017

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Isometry
Odd
Symmetric group
Wreath Product
Alternating group
Weyl Group
Isometric
Crossover
Finite Group
Cover
Analogue
Generalise

Cite this

Perfect Isometries and Murnaghan-Nakayama Rules. / Brunat, Olivier; Gramain, Jean-Baptiste.

In: Transactions of the American Mathematical Society, Vol. 369, No. 11, 2017, p. 7657-7718.

Research output: Contribution to journalArticle

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