English

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.

Keywords

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}
}

Comments

31 pages

R2 v1 2026-06-21T10:47:17.704Z