# Gelfand models for diagram algebras

@article{Halverson2013GelfandMF,
title={Gelfand models for diagram algebras},
author={Tom Halverson and Michael Reeks},
journal={Journal of Algebraic Combinatorics},
year={2013},
volume={41},
pages={229-255}
}
• Published 25 February 2013
• Mathematics
• Journal of Algebraic Combinatorics
A Gelfand model for a semisimple algebra $$\mathsf {A}$$A over an algebraically closed field $$\mathbb {K}$$K is a linear representation that contains each irreducible representation of $$\mathsf {A}$$A with multiplicity exactly one. We give a method of constructing these models that works uniformly for a large class of semisimple, combinatorial diagram algebras including the partition, Brauer, rook monoid, rook-Brauer, Temperley-Lieb, Motzkin, and planar rook monoid algebras. In each case, the…
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