Combinatorial Gelfand models for some semigroups and qrook monoid algebras
Abstract
Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebras of the symmetric inverse semigroup to a Gelfand model for the $q$rook monoid algebra.
 Publication:

arXiv eprints
 Pub Date:
 October 2007
 arXiv:
 arXiv:0710.1972
 Bibcode:
 2007arXiv0710.1972K
 Keywords:

 Mathematics  Representation Theory;
 16G10;
 20M20;
 20B30
 EPrint:
 14 pages