Perfect isometries and Murnaghan-Nakayama rules
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- by Olivier Brunat and Jean-Baptiste Gramain PDF
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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.References
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Additional Information
- Olivier Brunat
- Affiliation: Université Paris-Diderot Paris 7, Institut de mathématiques de Jussieu – Paris Rive Gauche, UFR de mathématiques, Case 7012, 75205 Paris Cedex 13, France
- Email: olivier.brunat@imj-prg.fr
- Jean-Baptiste Gramain
- Affiliation: Institute of Mathematics, University of Aberdeen, King’s College, Fraser Noble Building, Aberdeen AB24 3UE, United Kingdom
- Email: jbgramain@abdn.ac.uk
- Received by editor(s): April 2, 2014
- Received by editor(s) in revised form: November 10, 2014, March 10, 2015, June 12, 2015, July 6, 2015, August 28, 2015, September 23, 2015, October 8, 2015, and October 27, 2015
- Published electronically: May 11, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 7657-7718
- MSC (2010): Primary 20C30, 20C15; Secondary 20C20
- DOI: https://doi.org/10.1090/tran/6860
- MathSciNet review: 3695841