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Transactions of the American Mathematical Society

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

 
 

 

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
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
Article copyright: © Copyright 2014 American Mathematical Society