A Temperley-Lieb analogue for the BMW algebra
Representation Theory
2008-06-05 v1 Quantum Algebra
Abstract
The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl(2) on the n-th tensor power of the 2-dimensional irreducible module. We define and study a quotient of the Birman-Wenzl-Murakami algebra, which plays an analogous role for the 3-dimensional representation of quantum sl(2). In the course of the discussion we prove some general results about the radical of a cellular algebra, which may be of independent interest.
Cite
@article{arxiv.0806.0687,
title = {A Temperley-Lieb analogue for the BMW algebra},
author = {G. I. Lehrer and R. B. Zhang},
journal= {arXiv preprint arXiv:0806.0687},
year = {2008}
}
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31 pages