Affine Hecke algebras of type D and generalisations of quiver Hecke algebras

JOURNAL OF ALGEBRA

卷:552

Article

d'Andecy, L. Poulain¹  Walker, R.² 

[1] Uniyersite Reims Champagne Ardenne, Lab Math Reims, UMR 9008, F-51097 Reims, France

[2] Univ Paris Diderot Paris VII, Batiment Sophie Germain, F-75205 Paris 13, France

关键词: Affine Hecke algebras;    Quiver Hecke algebras;    Cyclotomic quotients;   

DOI  :  10.1016/j.jalgebra.2019.11.039

来源: Elsevier

【 摘 要 】

We define and study cyclotomic quotients of affine Hecke algebras of type D. We establish an isomorphism between (direct sums of blocks of) these cyclotomic quotients and a generalisation of cyclotomic quiver Hecke algebras which are a family of Z-graded algebras closely related to algebras introduced by Shan, Varagnolo and Vasserot. To achieve this, we first complete the study of cyclotomic quotients of affine Hecke algebras of type B by considering the situation when a deformation parameter p squares to 1. We then relate the two generalisations of quiver Hecke algebras showing that the one for type D can be seen as fixed point subalgebras of their analogues for type B, and we carefully study how far this relation remains valid for cyclotomic quotients. This allows us to obtain the desired isomorphism. This isomorphism completes the family of isomorphisms relating affine Hecke algebras of classical types to (generalisations of) quiver Hecke algebras, originating in the famous result of Brundan and Kleshchev for the type A. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free