Markov traces and generic degrees in type Bn

Lacrimioara Iancu

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)731-744
Number of pages14
JournalJournal of Algebra
Volume236
Issue number2
DOIs
Publication statusPublished - 15 Feb 2001

Cite this

Markov traces and generic degrees in type Bn. / Iancu, Lacrimioara.

In: Journal of Algebra, Vol. 236, No. 2, 15.02.2001, p. 731-744.

Research output: Contribution to journalArticle

Iancu, Lacrimioara. / Markov traces and generic degrees in type Bn. In: Journal of Algebra. 2001 ; Vol. 236, No. 2. pp. 731-744.
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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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