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 Sn-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.
Gelfand models and Robinson-Schensted correspondence / F. Caselli; R. Fulci. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - STAMPA. - 36:(2012), pp. 175-207. [10.1007/s10801-011-0328-y]
Gelfand models and Robinson-Schensted correspondence
CASELLI, FABRIZIO;FULCI, ROBERTA
2012
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 Sn-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.