On Representations of Affine Temperley--Lieb Algebras

Abstract

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 certain $q$-analogue of the annular algebra of V.F.R. Jones.

24 pages, 3 figures. This paper was published in 1998 in the Proceedings of the 8th International Conference on Representations of Algebras