Related papers: Representations of Temperley--Lieb Algebras
In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…
In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of…
The affine Temperley-Lieb algebra $\mathsf{a}\hskip-1.8pt\mathsf{TL}_{N}(\beta)$ is an infinite-dimensional algebra parametrized by a number $\beta \in \mathbb{C}$ and an integer $N\in \mathbb{N}$. It naturally acts on…
We introduce two new algebras that we call \emph{tied--boxed Hecke algebra} and \emph{tied--boxed Temperley--Lieb algebra}. The first one is a subalgebra of the algebra of braids and ties introduced by Aicardi and Juyumaya, and the second…
We show that the homology of a Temperley-Lieb algebra on an even number of strands has a rich algebraic structure and is highly nontrivial in general. This is achieved by proving that it is entirely governed by a differential graded…
In this paper, we will study the Dieck-Temlerley-Lieb algebras of type Bn and Cn. We compute their ranks and describe a basis for them by using some results from corresponding Brauer algebras and Temperley-Lieb algebras.
We investigate critical restricted solid-on-solid models associated to Dynkin diagrams of type $A$, $D$ and $E$, with fixed, periodic and twisted periodic boundary conditions. These models are endowed with an action of the diagrams of the…
This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…
We study representations of Temperley-Lieb algebras associated with the transfer matrix formulation of statistical mechanics on arbitrary lattices. We first discuss a new hyperfinite algebra, the Diagram algebra $D_{\underline{n}}(Q)$,…
The $A_{n-1}$ Gaudin model with integerable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding…
We consider two families of polynomials that play the same role in the Temperley Lieb algebra of a Coxeter group as the Kazhdan Lusztig and R polynomials play in the Hecke algebra of the group. We study these polynomials from a…
We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.
It is shown that the multiplicative monoids of Temperley-Lieb algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a…
Let $p$ denote a prime number. In this note, we focus on the modular Terwilliger algebras of association schemes defined in [3]. We define the primary module of a modular Terwilliger algebra of an association scheme and determine all its…
The hamiltonian of the $N$-state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by $N-1$ types of Temperley-Lieb generators. This generalises a previous result for $N=3$ obtained by J. F. Fjelstad…
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable…
Both the original Temperley-Lieb algebras $\mathsf{TL}_{n}$ and their dilute counterparts $\mathsf{dTL}_{n}$ form families of filtered algebras: $\mathsf{TL}_{n}\subset \mathsf{TL}_{n+1}$ and $\mathsf{dTL}_{n}\subset\mathsf{dTL}_{n+1}$, for…
In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley--Lieb algebra of type affine $C$, which has a basis indexed by the fully commutative elements of the Coxeter group of the…
The Kadar--Yu algebras are a physically motivated sequence of towers of algebras interpolating between the Brauer algebras and Temperley--Lieb algebras. The complex representation theory of the Brauer and Temperley--Lieb algebras is now…
We define a tower of affine Temperley-Lieb algebras of type $\tilde{A_{n}}$ and we define Markov elements in those algebras. We prove that any trace over an affine Temperley-Lieb algebras of type $\tilde{A_{2}}$ is uniquely defined by its…