Products of symmetric group characters

In [33], the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable Kronecker coefficients. In this paper we give combinatorial descriptions...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series A 2019-07, Vol.165, p.299-324
Main Authors: Orellana, Rosa, Zabrocki, Mike
Format: Article
Language:English
Subjects:
Kronecker product
Symmetric functions
Symmetric group representations
Tensor products
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Summary:In [33], the authors introduced a new basis of the ring of symmetric functions which evaluate to the irreducible characters of the symmetric group at roots of unity. The structure coefficients for this new basis are the stable Kronecker coefficients. In this paper we give combinatorial descriptions for several products. In addition, we identify some applications and instances where special cases of these products have occurred elsewhere in the mathematical literature.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2019.02.019