O. V. Ogievetsky, L. Poulain d`Andecy. Jucys-murphy elements and representations of cyclotomic Hecke algebras
Submitted on: Sep 12, 2012, 17:32:23
Natural Sciences / Mathematics / Algebra
Description: 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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