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Combinatorial Gelfand models for some semigroups and q-rook monoid algebras

Part of: Modules, bimodules and ideals Semigroups

Published online by Cambridge University Press:  23 September 2009

Ganna Kudryavtseva  and
Volodymyr Mazorchuk
Ganna Kudryavtseva
Affiliation:
Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 64 Volodymyrska St., 01033 Kyiv, Ukraine; Email: ([email protected])
Volodymyr Mazorchuk
Affiliation:
Department of Mathematics, Uppsala University, SE 47106 Uppsala, Sweden; Email: ([email protected]
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Abstract

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Inspired by the results of Adin, Postnikov and Roichman, 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.

Keywords

Gelfand modelrook monoidinverse semigroupinvolution

MSC classification

Secondary: 20M30: Representation of semigroups; actions of semigroups on sets 20M20: Semigroups of transformations, etc. 16D60: Simple and semisimple modules, primitive rings and ideals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 707 - 718
Copyright
Copyright © Edinburgh Mathematical Society 2009