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Kleshchev's decomposition numbers for diagrammatic Cherednik algebras


Authors: C. Bowman and L. Speyer
Journal: Trans. Amer. Math. Soc. 370 (2018), 3551-3590
MSC (2010): Primary 05E10, 20C08, 20C30
DOI: https://doi.org/10.1090/tran/7054
Published electronically: December 20, 2017
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Abstract | References | Similar Articles | Additional Information

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
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
Email: l.speyer@virginia.edu

DOI: https://doi.org/10.1090/tran/7054
Received by editor(s): July 28, 2015
Received by editor(s) in revised form: August 12, 2016
Published electronically: December 20, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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