diagram algebra
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2018 ◽  
Vol 50 (2) ◽  
pp. 191-224
Author(s):  
Robert P. Laudone
Keyword(s):  

Knot Theory ◽  
2018 ◽  
pp. 239-258
Author(s):  
Vassily Manturov

2017 ◽  
pp. 155-169
Author(s):  
Lyubomir T. Gruyitch

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Tom Halverson

International audience A Gelfand model for a semisimple algebra $\mathsf{A}$ over $\mathbb{C}$ is a complex linear representation that contains each irreducible representation of $\mathsf{A}$ with multiplicity exactly one. We give a method of constructing these models that works uniformly for a large class of combinatorial diagram algebras including: the partition, Brauer, rook monoid, rook-Brauer, Temperley-Lieb, Motzkin, and planar rook monoid algebras. In each case, the model representation is given by diagrams acting via ``signed conjugation" on the linear span of their vertically symmetric diagrams. This representation is a generalization of the Saxl model for the symmetric group, and, in fact, our method is to use the Jones basic construction to lift the Saxl model from the symmetric group to each diagram algebra. In the case of the planar diagram algebras, our construction exactly produces the irreducible representations of the algebra.


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