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arXiv · 1206.0612

Jucys--Murphy elements and representations of cyclotomic Hecke algebras

O. V. Ogievetsky·L. Poulain d'Andecy
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Abstract

An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using representations of the simplest affine Hecke algebra. Representations are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by standard m-tableaux.

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BibTeXRIS

O. V. Ogievetsky, L. Poulain d'Andecy. 2012-06-18. Jucys--Murphy elements and representations of cyclotomic Hecke algebras. https://arxiv.org/abs/1206.0612

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