Jucys--Murphy elements and representations of cyclotomic Hecke algebras
Representation Theory
2012-06-19 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1206.0612,
title = {Jucys--Murphy elements and representations of cyclotomic Hecke algebras},
author = {O. V. Ogievetsky and L. Poulain d'Andecy},
journal= {arXiv preprint arXiv:1206.0612},
year = {2012}
}
Comments
51 pages