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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cyclotomic quiver Hecke algebras and Hecke algebra of $G(r,p,n)$
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by Salim Rostam PDF
Trans. Amer. Math. Soc. 371 (2019), 3877-3916 Request permission

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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Additional Information
  • Salim Rostam
  • Affiliation: Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France
  • MR Author ID: 1204275
  • Email: salim.rostam@ens-rennes.fr
  • Received by editor(s): November 12, 2016
  • Received by editor(s) in revised form: September 28, 2017
  • Published electronically: November 16, 2018
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 3877-3916
  • MSC (2010): Primary 20C08
  • DOI: https://doi.org/10.1090/tran/7485
  • MathSciNet review: 3917212