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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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Kleshchev’s decomposition numbers for diagrammatic Cherednik algebras
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by C. Bowman and L. Speyer PDF
Trans. Amer. Math. Soc. 370 (2018), 3551-3590 Request permission

Abstract:

We construct a family of graded isomorphisms between certain subquotients of diagrammatic Cherednik algebras as the quantum characteristic, multicharge, level, degree, and weighting are allowed to vary; this provides new structural information even in the case of the classical $q$-Schur algebra. This also allows us to prove some of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic.
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Additional Information
  • C. Bowman
  • Affiliation: Department of Mathematics, City University London, Northampton Square, London, EC1V 0HB, United Kingdom
  • Address at time of publication: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, United Kingdom
  • MR Author ID: 922280
  • Email: c.d.bowman@kent.ac.uk
  • L. Speyer
  • Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan
  • Address at time of publication: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
  • MR Author ID: 1076718
  • Email: l.speyer@virginia.edu
  • Received by editor(s): July 28, 2015
  • Received by editor(s) in revised form: August 12, 2016
  • Published electronically: December 20, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3551-3590
  • MSC (2010): Primary 05E10, 20C08, 20C30
  • DOI: https://doi.org/10.1090/tran/7054
  • MathSciNet review: 3766858