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Transactions of the American Mathematical Society

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


Author: Salim Rostam
Journal: Trans. Amer. Math. Soc. 371 (2019), 3877-3916
MSC (2010): Primary 20C08
DOI: https://doi.org/10.1090/tran/7485
Published electronically: November 16, 2018
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Abstract: 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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Salim Rostam
Affiliation: Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France
Email: salim.rostam@ens-rennes.fr

DOI: https://doi.org/10.1090/tran/7485
Received by editor(s): November 12, 2016
Received by editor(s) in revised form: September 28, 2017
Published electronically: November 16, 2018
Article copyright: © Copyright 2018 American Mathematical Society