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Affine Hecke algebras and generalizations of quiver Hecke algebras of type B

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 March 2020

L. Poulain d'Andecy  and
R. Walker
L. Poulain d'Andecy
Affiliation:
Laboratoire de Mathématiques de Reims UMR 9008, Université de Reims Champagne-Ardenne, UFR Sciences Exactes et Naturelles, Moulin de la Housse BP 1039, 51100Reims, France (loic.poulain-dandecy@univ-reims.fr)
R. Walker
Affiliation:
Université Paris Diderot-Paris VII, Bâtiment Sophie Germain, 75205Paris Cedex 13, France (ruari.walker@imj-prg.fr)
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Abstract

We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalization, for type B, of cyclotomic quiver Hecke algebras, which are a family of graded algebras closely related to algebras introduced by Varagnolo and Vasserot. Inspired by the work of Brundan and Kleshchev, we first give a family of isomorphisms for the corresponding result in type A which includes their original isomorphism. We then select a particular isomorphism from this family and use it to prove our result.

Keywords

Affine Hecke algebrasKLR algebrasquiver Hecke algebras

MSC classification

Primary: 20C08: Hecke algebras and their representations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 2 , May 2020 , pp. 531 - 578
Copyright
Copyright © Edinburgh Mathematical Society 2020

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References

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