### 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 | |

Publication status | Published - 15 Feb 2001 |

### Cite this

*B*.

_{n}*Journal of Algebra*,

*236*(2), 731-744. https://doi.org/10.1006/jabr.2000.8523

**Markov traces and generic degrees in type B_{n}.** / Iancu, Lacrimioara.

Research output: Contribution to journal › Article

*B*',

_{n}*Journal of Algebra*, vol. 236, no. 2, pp. 731-744. https://doi.org/10.1006/jabr.2000.8523

*B*. Journal of Algebra. 2001 Feb 15;236(2):731-744. https://doi.org/10.1006/jabr.2000.8523

_{n}}

TY - JOUR

T1 - Markov traces and generic degrees in type Bn

AU - Iancu, Lacrimioara

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.

PY - 2001/2/15

Y1 - 2001/2/15

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.

U2 - 10.1006/jabr.2000.8523

DO - 10.1006/jabr.2000.8523

M3 - Article

VL - 236

SP - 731

EP - 744

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -