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From the same journal

Multiplicity-free Kronecker products of characters of the symmetric groups

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Publication details

JournalAdvances in Mathematics
DateAccepted/In press - 10 Oct 2017
DateE-pub ahead of print - 13 Nov 2017
DatePublished (current) - 15 Dec 2017
Volume322
Number of pages57
Pages (from-to)473-529
Early online date13/11/17
Original languageEnglish

Abstract

We provide a classification of multiplicity-free inner tensor products of irreducible characters of symmetric groups, thus confirming a conjecture of Bessenrodt. Concurrently, we classify all multiplicity-free inner tensor products of skew characters of the symmetric groups. We also provide formulae for calculating the decomposition of these tensor products.

Bibliographical note

Funding Information:
We would like to thank the American Institute of Mathematics and the organisers of “Combinatorics and complexity of Kronecker coefficients” and Banff International Research Station for their hospitality. We would also like to thank Leibniz Universität Hannover , EPSRC grant EP/L01078X/1 , and the Royal Commission for the Exhibition of 1851 for their financial support towards mutual visits in Hannover and London. We are grateful to John Stembridge for sharing his Maple package SF that was helpful for computations. We would like to thank S. Assaf, A. Hicks, J. Remmel, V. Tewari, and S. van Willigenburg for their interest at some stages of this project. Thanks go to M. Wildon for asking us about Theorem 1.2 during the conference “Kronecker Coefficients 2016”. Finally, we would like to thank the referee for many helpful comments and suggestions.

Publisher Copyright:
© 2017

    Research areas

  • Irreducible characters, Kronecker coefficients, Symmetric groups, Tensor products

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