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Affine Hecke algebras of type D and generalisations of quiver Hecke algebras
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-06-01 , DOI: 10.1016/j.jalgebra.2019.11.039
L. Poulain d'Andecy , R. Walker

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.

中文翻译:

D 类仿射 Hecke 代数和 quiver Hecke 代数的推广

我们定义并研究了 D 类仿射 Hecke 代数的圈商。我们建立了这些圈商(块的直接和)之间的同构和圈圈 quiver Hecke 代数的推广,后者是与代数密切相关的 Z 级代数族由 Shan、Varagnolo 和 Vasserot 介绍。为了实现这一点,我们首先通过考虑变形参数 p 平方为 1 的情况来完成对 B 类仿射 Hecke 代数的分圆商的研究。然后我们将 quiver Hecke 代数的两个推广联系起来,表明 D 类可以被视为 B 型类似物的不动点子代数,我们仔细研究了这种关系在多大程度上对分圆商仍然有效。这使我们能够获得所需的同构。
更新日期:2020-06-01
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