Morita equivalences for cyclotomic Hecke algebras of type B and D

Abstract

We give a Morita equivalence theorem for so-called cyclotomic quotients of affine Hecke algebras of type B and D, in the spirit of a classical result of Dipper-Mathas in type A for Ariki-Koike algebras. As a consequence, the representation theory of affine Hecke algebras of type B and D reduces to the study of their cyclotomic quotients with eigenvalues in a single orbit under multiplication by $q^2$ and inversion. The main step in the proof consists in a decomposition theorem for generalisations of quiver Hecke algebras that appeared recently in the study of affine Hecke algebras of type B and D. This theorem reduces the general situation of a disconnected quiver with involution to a simpler setting. To be able to treat types B and D at the same time we unify the different definitions of generalisations of quiver Hecke algebra for type B that exist in the literature.

arXiv comment42 pages. v2: the statements for type D are corrected. v3: final version. To appear in Bull. SMF

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Cited by in corpus (4)

• Representations of orientifold Khovanov-Lauda-Rouquier algebras and the Enomoto-Kashiwara algebra
• Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
• Affine Hecke algebras of type D and generalisations of quiver Hecke algebras
• Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups