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ON REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS

Center of Theoretical Physics, Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix–Marseille I, Aix–Marseille II et du Sud Toulon – Var; laboratoire affilié à la FRUMAM (FR 2291), Luminy 13288 Marseille, France

J.-V. Poncelet French-Russian Laboratory, UMI 2615 du CNRS, Independent University of Moscow, 11 B. Vlasievski per., 119002 Moscow, Russia

On leave of absence from P. N. Lebedev Physical Institute, Leninsky Pr. 53, 117924 Moscow, Russia.

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L. POULAIN D'ANDECY

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https://doi.org/10.1142/S0217732311035377Cited by:9 (Source: Crossref)

Abstract

An approach, based on Jucys–Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys–Murphy elements is established. A basis of the cyclotomic Hecke algebra is suggested; this basis is used to establish the flatness of the deformation without using the representation theory.

Keywords:

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