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Markov traces on cyclotomic Temperley–Lieb algebras

Author: Hebing Rui
Journal: Proc. Amer. Math. Soc. 134 (2006), 2873-2880
MSC (2000): Primary 16S99, 16K20
Published electronically: May 5, 2006
MathSciNet review: 2231610
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Abstract: In this note, we use generalized Tchebychev polynomials to define a trace function which satisfies certain conditions. Such a trace will be called the Markov trace. In particular, we obtain formulae for the weights of the Markov trace. As a corollary, we get a combinatorial identity. This generalizes Jones’s 1983 result on Temperley–Lieb algebras.

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Hebing Rui
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China

Received by editor(s): November 17, 2004
Received by editor(s) in revised form: March 12, 2005, and May 7, 2005
Published electronically: May 5, 2006
Additional Notes: The author was partially supported by NSFC no. 10331030 and JSPS. He wishes to thank the Research Institute for Mathematical Sciences, Kyoto University, for its hospitality during his visit
Communicated by: John R. Stembridge
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.