Affine Hecke algebras and generalizations of quiver Hecke algebras of type B. Issue 2 (9th May 2020) - Poulain d'Andecy, L.; Walker, R.
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.