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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on certain Kronecker coefficients
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by L. Manivel PDF
Proc. Amer. Math. Soc. 138 (2010), 1-7 Request permission

Abstract:

We prove an explicit formula for the tensor square of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of representations defined by rectangles of heights two and four. Our results are deduced, through Schur-Weyl duality, from the observation that certain actions on triple tensor products of vector spaces are multiplicity free.
References
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Additional Information
  • L. Manivel
  • Affiliation: Institut Fourier, University of Grenoble I, 100 rue des Mathematiques, 38402 St. Martin d’Heres, France
  • MR Author ID: 291751
  • ORCID: 0000-0001-6235-454X
  • Received by editor(s): October 8, 2008
  • Published electronically: September 4, 2009
  • Communicated by: Jonathan I. Hall
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 1-7
  • MSC (2000): Primary 20C30, 15A72, 11S90
  • DOI: https://doi.org/10.1090/S0002-9939-09-10086-2
  • MathSciNet review: 2550164