Affine Hecke algebras and generalizations of quiver Hecke algebras of type B. Issue 2 (9th May 2020)

• Record Type: Journal Article
• Authors: Poulain d'Andecy, L.; Walker, R.
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 63:Issue 2(2020)
• Page Start: 531
• Page End: 578
• Publication Date: 2020-05-09
• Subjects: Affine Hecke algebras, -- KLR algebras, -- quiver Hecke algebras; 20C08; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091519000294
• Languages: English
• ISSNs: 0013-0915

Abstract

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.