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

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

2007-04-02

arxiv.org/abs/0704.0283v1

Mathematics

Quantum Algebra

Approximately 37 pages, AMSTeX. 9 figures.

Scientific paper

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 $n \geq 6$). 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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