Simple modules for Temperley-Lieb algebras and related algebras

JOURNAL OF ALGEBRA

卷:520

Article

关键词: Representation theory;    Quantum groups;    Temperley-Lieb algebras;   

DOI  :  10.1016/j.jalgebra.2018.10.035

来源: Elsevier

【 摘 要 】

Let k be an arbitrary field and let q is an element of k\ {0}. In this paper we use the known tilting theory for the quantum group U-q (sl(2)) to obtain the dimensions of simple modules for the Temperley-Lieb algebras TLn(q+q(-1)) and related algebras over k. Our main result is an algorithm which calculates the dimensions of simple modules for these algebras. We take advantage of the fact that TLn(q+q(-1)) is isomorphic to the endomorphism ring of the n'th tensor power of the natural 2-dimensional module for the quantum group for sl(2). This algorithm is easy when the characteristic is 0 and more involved in positive characteristic. We point out that our results for the Temperley-Lieb algebras contain a complete description of the simple modules for the Jones quotient algebras. Moreover, we illustrate how the same results lead to corresponding information about simple modules for the BMW-algebras with special parameters and other algebras closely related with endomorphism algebras of families of tilting modules for if U-q (sl(2)). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free