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arXiv · 1501.06389

An isomorphism Theorem for Yokonuma--Hecke algebras and applications to link invariants

N. Jacon·L. Poulain d'Andecy
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Abstract

We develop several applications of the fact that the Yokonuma--Hecke algebra of the general linear group GL is isomorphic to a direct sum of matrix algebras associated to Iwahori--Hecke algebras of type A. This includes a description of the semisimple and modular representation theory of the Yokonuma--Hecke algebras of GL and a complete classification of all the Markov traces for them. Finally, from these Markov traces, we construct 3-variables polynomials which are invariants for framed and classical knots and links, and investigate their properties with the help of the isomorphism.

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BibTeXRIS

N. Jacon, L. Poulain d'Andecy. 2015-10-07. An isomorphism Theorem for Yokonuma--Hecke algebras and applications to link invariants. https://arxiv.org/abs/1501.06389

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