Markov traces and generic degrees in type Bn

Lacrimioara Iancu

doi:10.1006/jabr.2000.8523

Markov traces and generic degrees in type B_n

Lacrimioara Iancu

Mathematical Science

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori-Hecke algebra H-n of type B-n. These traces depend on two parameters and are linear combinations of the irreducible characters of H-n, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices or the parameters. In this article, we derive from Orellana's result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmit's formulas for the generic degrees of H-n. Finally, we present a conjectural formula for weights of Markov traces on Ariki-Koike algebras. (C) 2001 Academic Press.

Original language	English
Pages (from-to)	731-744
Number of pages	14
Journal	Journal of Algebra
Volume	236
Issue number	2
DOIs	https://doi.org/10.1006/jabr.2000.8523
Publication status	Published - 15 Feb 2001

Bibliographical note

The idea that Orellana’s results might lead to a new proof of Hoefsmit’s theorem and, suitably generalized, also to a proof of Malle’s conjecture, is due to Meinolf Geck. I thank him for sharing this idea with me and for many useful discussions.

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Cite this

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title = "Markov traces and generic degrees in type Bn",

abstract = "Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori-Hecke algebra H-n of type B-n. These traces depend on two parameters and are linear combinations of the irreducible characters of H-n, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices or the parameters. In this article, we derive from Orellana's result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmit's formulas for the generic degrees of H-n. Finally, we present a conjectural formula for weights of Markov traces on Ariki-Koike algebras. (C) 2001 Academic Press.",

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N1 - The idea that Orellana’s results might lead to a new proof of Hoefsmit’s theorem and, suitably generalized, also to a proof of Malle’s conjecture, is due to Meinolf Geck. I thank him for sharing this idea with me and for many useful discussions.

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N2 - Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori-Hecke algebra H-n of type B-n. These traces depend on two parameters and are linear combinations of the irreducible characters of H-n, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices or the parameters. In this article, we derive from Orellana's result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmit's formulas for the generic degrees of H-n. Finally, we present a conjectural formula for weights of Markov traces on Ariki-Koike algebras. (C) 2001 Academic Press.

AB - Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori-Hecke algebra H-n of type B-n. These traces depend on two parameters and are linear combinations of the irreducible characters of H-n, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices or the parameters. In this article, we derive from Orellana's result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmit's formulas for the generic degrees of H-n. Finally, we present a conjectural formula for weights of Markov traces on Ariki-Koike algebras. (C) 2001 Academic Press.

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DO - 10.1006/jabr.2000.8523

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