# 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} }

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…

## 13 Citations

### Set-partition tableaux and representations of diagram algebras

- Mathematics
- 2018

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras…

### G(l,k,d)-modules via groupoids

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- 2014

In this note we describe a seemingly new approach to the complex representation theory of the wreath product $G\wr S_d$ where $G$ is a finite abelian group. The approach is motivated by an…

### $$G(\ell ,k,d)$$G(ℓ,k,d)-modules via groupoids

- Mathematics
- 2016

In this note, we describe a seemingly new approach to the complex representation theory of the wreath product $$G\wr S_d$$G≀Sd, where G is a finite abelian group. The approach is motivated by an…

### Multiparameter colored partition category and the product of the reduced Kronecker coefficients

- Mathematics
- 2022

A BSTRACT . We introduce and study a multiparameter colored partition category CPar ( x ) by extending the construction of the partition category, over an algebraically closed ﬁeld 𝕜 of…

### G ( , k , d )-modules via groupoids

- Mathematics
- 2014

In this note, we describe a seemingly new approach to the complex representation theory of the wreath product G Sd , where G is a finite abelian group. The approach is motivated by an appropriate…

### Jucys–Murphy elements and Grothendieck groups for generalized rook monoids

- MathematicsJournal of Combinatorial Algebra
- 2022

. We consider a tower of generalized rook monoid algebras over the ﬁeld C of complex numbers and observe that the Bratteli diagram associated to this tower is a simple graph. We construct simple…

### Combinatorial Gelfand Models for Semisimple Diagram Algebras

- MathematicsMilan Journal of Mathematics
- 2013

We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras,…

### Combinatorial Gelfand Models for Semisimple Diagram Algebras

- Mathematics
- 2013

We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras,…

### Tensor power multiplicities for symmetric and alternating groups and dimensions of irreducible modules for partition algebras

- Mathematics
- 2016

The partition algebra $\mathsf{P}_k(n)$ and the symmetric group $\mathsf{S}_n$ are in Schur-Weyl duality on the $k$-fold tensor power $\mathsf{M}_n^{\otimes k}$ of the permutation module…

### Connecting Permutation Equivariant Neural Networks and Partition Diagrams

- Mathematics, Computer ScienceArXiv
- 2022

We show how the Schur–Weyl duality that exists between the partition algebra and the symmetric group results in a stronger theoretical foundation for characterising all of the possible permutation…

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