Gelfand models and Robinson-Schensted correspondence

2011/01/26 by Caselli, Fabrizio, Fulci, Roberta
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1101.5021

Abstract

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model 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.

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