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An isomorphism theorem for Yokonuma–Hecke algebras and applications to link invariants

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...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2016-06, Vol.283 (1-2), p.301-338
Main Authors: Jacon, N., Poulain d’Andecy, L.
Format: Article
Language:English
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Summary: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. In particular, for classical knots, a consequence of the construction is that the obtained set of invariants is topologically equivalent to the HOMFLYPT polynomial. We thus recover results of Chlouveraki et al. ( 2015 , arXiv:1505.06666 ) about the Juyumaya–Lambropoulou invariants.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-015-1598-1