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 noteFunding 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.
- Irreducible characters
- Kronecker coefficients
- Symmetric groups
- Tensor products