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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2019

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

Algèbres de Hecke cyclotomiques et algèbres de Hecke de G(r,p,n)

Résumé

Given a quiver automorphism with nice properties, we give a presentation of the fixed point 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 addition, we give an explicit isomorphism which realises a well-known Morita equivalence between Ariki–Koike algebras.
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Dates et versions

hal-01794939 , version 1 (18-05-2018)
hal-01794939 , version 2 (20-12-2018)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

Citer

Salim Rostam. Cyclotomic quiver Hecke algebras and Hecke algebra of G(r,p,n). Transactions of the American Mathematical Society, 2019, 371 (6), pp.3877-3916. ⟨10.1090/tran/7485⟩. ⟨hal-01794939v1⟩
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