On the Markov trace for Temperley--Lieb algebras of type E_n

2007/04/02 by Green, R. M.
#20C08 #20F55 #57M15 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.0704.0283

Abstract

We show that there is a unique Markov trace on the tower of Temperley--Lieb type quotients of Hecke algebras of Coxeter type E_n (for all n ≥ 6). We explain in detail how this trace may be computed easily using tom Dieck's calculus of diagrams. As applications, we show how to use the trace to show that the diagram representation is faithful, and to compute leading coefficients of certain Kazhdan--Lusztig polynomials.

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• Markov elements in affine Temperley-Lieb algebras
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• Weights of Markov Traces on Hecke algebras