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.
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 language | English |
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Pages (from-to) | 7657-7718 |
Number of pages | 62 |
Journal | Transactions of the American Mathematical Society |
Volume | 369 |
Issue number | 11 |
Early online date | 11 May 2017 |
DOIs | |
Publication status | Published - Nov 2017 |
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-
Jean-Baptiste Gramain
- School of Natural & Computing Sciences, Mathematical Science - Senior Lecturer
Person: Academic