ON REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS-Reference-Cited by-同舟云学术

ON REPRESENTATIONS OF CYCLOTOMIC HECKE ALGEBRAS

Published:2011-04-10 Issue:11 Volume:26 Page:795-803
ISSN:0217-7323
Container-title:Modern Physics Letters A
language:en
Short-container-title:Mod. Phys. Lett. A

Author:

OGIEVETSKY O. V.¹²,POULAIN D'ANDECY L.¹

Affiliation:

1. 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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Physics and Astronomy,Astronomy and Astrophysics,Nuclear and High Energy Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217732311035377

Reference5 articles.

1. A Hecke Algebra of (Z/rZ)Sn and Construction of Its Irreducible Representations

2. On the Semi-simplicity of the Hecke Algebra of (Z/rZ) ≀ Sn

3. On baxterized solutions of reflection equation and integrable chain models

4. On representations of Hecke algebras

5. A new approach to representation theory of symmetric groups

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