SIGMA 10 (2014), 039, 13 pages      arXiv:1301.4237      https://doi.org/10.3842/SIGMA.2014.039
Contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa

Fusion Procedure for Cyclotomic Hecke Algebras

Oleg V. Ogievetsky ^{a, b, c} and Loïc Poulain d'Andecy ^d
a) Center of Theoretical Physics, Aix Marseille Université, CNRS, UMR 7332, 13288 Marseille, France
^b) Université de Toulon, CNRS, UMR 7332, 83957 La Garde, France
^c) On leave of absence from P.N. Lebedev Physical Institute, Leninsky Pr. 53, 117924 Moscow, Russia
^d) Mathematics Laboratory of Versailles, LMV, CNRS UMR 8100, Versailles Saint-Quentin University, 45 avenue des Etas-Unis, 78035 Versailles Cedex, France

Received September 28, 2013, in final form March 29, 2014; Published online April 01, 2014

Abstract
A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a product of two terms, one of which depends only on the shape of the multi-tableau and is proportional to the inverse of the corresponding Schur element.

Key words: cyclotomic Hecke algebras; fusion formula; idempotents; Young tableaux; Jucys-Murphy elements; Schur element.

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