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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The partition algebra and the Kronecker coefficients
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by C. Bowman, M. De Visscher and R. Orellana PDF
Trans. Amer. Math. Soc. 367 (2015), 3647-3667 Request permission

Abstract:

We propose a new approach to study the Kronecker coefficients by using the Schur–Weyl duality between the symmetric group and the partition algebra. We explain the limiting behaviour and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the reduced Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition.
References
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Additional Information
  • C. Bowman
  • Affiliation: Institut de Mathématiques de Jussieu, 5 rue du Thomas Mann, 75013, Paris, France
  • MR Author ID: 922280
  • Email: Bowman@math.jussieu.fr
  • M. De Visscher
  • Affiliation: Centre for Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, England
  • MR Author ID: 703480
  • Email: Maud.Devisscher.1@city.ac.uk
  • R. Orellana
  • Affiliation: Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, New Hampshire 03755
  • Email: Rosa.C.Orellana@dartmouth.edu
  • Received by editor(s): March 6, 2013
  • Received by editor(s) in revised form: June 10, 2013, and July 4, 2013
  • Published electronically: December 11, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 3647-3667
  • MSC (2010): Primary 20C30, 05E10
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06245-4
  • MathSciNet review: 3314819