A Temperley-Lieb analogue for the BMW algebra

Details A Temperley-Lieb analogue for the BMW algebra A Temperley-Lieb analogue for the BMW algebra

2008-06-04

arxiv.org/abs/0806.0687v1

Mathematics

Representation Theory

31 pages

Scientific paper

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.

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