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The partition algebra and the Kronecker coefficients


Authors: C. Bowman, M. De Visscher and R. Orellana
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
Published electronically: December 11, 2014
MathSciNet review: 3314819
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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.


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Additional Information

C. Bowman
Affiliation: Institut de Mathématiques de Jussieu, 5 rue du Thomas Mann, 75013, Paris, France
Email: Bowman@math.jussieu.fr

M. De Visscher
Affiliation: Centre for Mathematical Science, City University London, Northampton Square, London, EC1V 0HB, England
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

DOI: https://doi.org/10.1090/S0002-9947-2014-06245-4
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
Article copyright: © Copyright 2014 American Mathematical Society