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JOURNAL OF
ALGEBRAIC
COMBINATORICS
  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Gelfand models and Robinson-Schensted correspondence

Fabrizio Caselli and Roberta Fulci
Dipartimento di Matematica, Universitá di Bologna, Bologna, Italy

DOI: 10.1007/s10801-011-0328-y

Abstract

In F. Caselli (Involutory reflection groups and their models, J. Algebra 24:370-393, 2010), a uniform Gelfand model is constructed for all nonexceptional irreducible complex reflection groups which are involutory. Such models can be naturally decomposed into the direct sum of submodules indexed by S n -conjugacy classes, and we present here a general result that relates the irreducible decomposition of these submodules with the projective Robinson-Schensted correspondence. This description also reflects, in a very explicit way, the existence of split representations for these groups.

Pages: 175–207

Keywords: complex reflection groups; characters and representations of finite groups; Clifford theory

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References

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