# 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.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-02104136
Contributor : Salim Rostam <>
Submitted on : Friday, April 19, 2019 - 12:12:25 PM
Last modification on : Thursday, May 16, 2019 - 1:21:03 AM

### Files

arXiv_v2.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02104136, version 1
• ARXIV : 1903.01580

### Citation

Loïc Poulain d'Andecy, Salim Rostam. Morita equivalences for cyclotomic Hecke algebras of type B and D. 2019. ⟨hal-02104136⟩

Record views