This article is cited in 7 papers

Fusion Procedure for Cyclotomic Hecke Algebras

Oleg V. Ogievetsky^abc, Loïc Poulain d'Andecy<sup>d

a</sup> Center of Theoretical Physics, Aix Marseille Université, CNRS, UMR 7332, 13288 Marseille, France
^b On leave of absence from P. N. Lebedev Physical Institute, Leninsky Pr. 53, 117924 Moscow, Russia
^c Université de Toulon, CNRS, UMR 7332, 83957 La Garde, France
^d Mathematics Laboratory of Versailles, LMV, CNRS UMR 8100, Versailles Saint-Quentin University, 45 avenue des Etas-Unis, 78035 Versailles Cedex, France

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.

Keywords: cyclotomic Hecke algebras; fusion formula; idempotents; Young tableaux; Jucys–Murphy elements; Schur element.

MSC: 20C08; 05E10

Received: September 28, 2013; in final form March 29, 2014; Published online April 1, 2014

Language: English

DOI: 10.3842/SIGMA.2014.039

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ArXiv: 1301.4237