Abstract
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 - 2017 |
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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 journal › Article
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TY - JOUR
T1 - Perfect Isometries and Murnaghan-Nakayama Rules
AU - Brunat, Olivier
AU - Gramain, Jean-Baptiste
N1 - Acknowledgement The 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.
PY - 2017
Y1 - 2017
N2 - This article is concerned with perfect isometries between blocksof finite groups. Generalizing a method of Enguehard to show that any twop-blocks of (possibly different) symmetric groups with the same weight areperfectly isometric, we prove analogues of this result for p-blocks of alternatinggroups (where the blocks must also have the same sign when p is odd), ofdouble covers of alternating and symmetric groups (for p odd, and where weobtain crossover isometries when the blocks have opposite signs), of complexreflection groups G(d, 1, n) (for d prime to p), of Weyl groups of type B andD (for p odd), and of certain wreath products. In order to do this, we needto generalize the theory of blocks in a way which should be of independentinterest.
AB - This article is concerned with perfect isometries between blocksof finite groups. Generalizing a method of Enguehard to show that any twop-blocks of (possibly different) symmetric groups with the same weight areperfectly isometric, we prove analogues of this result for p-blocks of alternatinggroups (where the blocks must also have the same sign when p is odd), ofdouble covers of alternating and symmetric groups (for p odd, and where weobtain crossover isometries when the blocks have opposite signs), of complexreflection groups G(d, 1, n) (for d prime to p), of Weyl groups of type B andD (for p odd), and of certain wreath products. In order to do this, we needto generalize the theory of blocks in a way which should be of independentinterest.
U2 - 10.1090/tran/6860
DO - 10.1090/tran/6860
M3 - Article
VL - 369
SP - 7657
EP - 7718
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 11
ER -