Markov traces on cyclotomic Temperley–Lieb algebras
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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.References
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Additional Information
- Hebing Rui
- Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
- Email: hbrui@math.ecnu.edu.cn
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 2873-2880
- MSC (2000): Primary 16S99, 16K20
- DOI: https://doi.org/10.1090/S0002-9939-06-08327-4
- MathSciNet review: 2231610