Related papers: On an algebraic approach to higher dimensional sta…

We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…

In an earlier work, we defined a ``generalised Temperley-Lieb algebra'' $TL_{r,1,n}$ corresponding to the imprimitive reflection group $G(r,1,n)$ as a quotient of the cyclotomic Hecke algebra. In this work we introduce the generalised…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have…

The authors of cond-mat/9911072 claim to introduce "new representations of the Hecke algebra." These representations are shown to be the XXC models introduced two years ago in solv-int/9712008, and repeatedly studied and referred to in…

We study the representation theory of the Temperley-Lieb algebra $\mathsf{TL}_n^k(\delta)$ in mixed characteristic, i.e. over an arbitrary field $k$ of characteristic $p$ and where $\delta$ satisfies some minimal polynomial $m_\delta$. In…

In this article we study higher homological properties of $n$-levelled algebras and connect them to properties of the underlying graphs. Notably, to each $2$-representation-finite quadratic monomial algebra $\Lambda$ we associate a…

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…

The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…

Left invariant affine structures in a Lie group $G$ are in one-to-one correspondence with left-symmetric algebras over its Lie algebra $\mathfrak g=T_eG$ (``over'' means that the commutator $[x,y]=xy-yx$ coincides with the Lie bracket;…

This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of this integrable model are briefly reviewed and then connected…

We study the finite-dimensional simple modules, over an algebraically closed field, of the affine Temperley--Lieb algebra corresponding to the affine Weyl group of type $A$. These turn out to be closely related to the simple modules for a…

We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the…

Orthogonal projections in ${\mathbb C}^n \otimes {\mathbb C}^n$ of rank one and rank two that give rise to unitary tensor space representations of the Temperley-Lieb algebra $TL_N(Q)$ are considered. In the rank one case, a complete…

Let $G$ be a finite group. There is a standard theorem on the classification of $G$-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of…

Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are…

For generic $q$ we give expressions for the transformations of all essentially typical finite-dimensional modules of the Hopf superalgebra $U_q[gl(3/2)]$. The latter is a deformation of the universal enveloping algebra of the Lie…

Affine and periodic Temperley-Lieb algebras are families of diagrammatic algebras that find diverse applications in mathematics and physics. These algebras are infinite dimensional, yet most of their interesting modules are finite. In this…

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

Let g be a basic classical Lie superalgebra over C. In the case of a typical weight whose every nonnegative integer multiple is also typical, we compute a closed form for the Hilbert series whose coefficients encode the dimensions of…