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 |
|---|---|
| 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 |
Bibliographical note
AcknowledgementThe authors wish to thank the referee for a very careful and precise reading
of several earlier versions of this manuscript. They are grateful for the number,
quality and helpfulness of comments and suggestions received.
