Cyclotomic quiver Hecke algebras and Hecke algebra of G(r,p,n)

Abstract

Given a quiver automorphism with nice properties, we give a presentation of the fixed subalgebra of the associated cyclotomic quiver Hecke algebra. Generalising an isomorphism of Brundan and Kleshchev between the cyclotomic Hecke algebra of type G(r,1,n) and the cyclotomic quiver Hecke algebra of type A, we apply the previous result to find a presentation of the cyclotomic Hecke algebra of type G(r,p,n) which looks very similar to the one of a cyclotomic quiver Hecke algebra. In the meanwhile, we give an explicit isomorphism which realises a well-known Morita equivalence between Ariki-Koike algebras.

35 pages, 2 figures. v2: include suggestions and minor corrections from the referee. Final version, to appear in Transactions of the AMS. v3: minor changes

Cited by in corpus (1)

• Skew cellularity of the Hecke algebras of type $G(\ell ,p,n)$