Skip to Main content Skip to Navigation
Conference papers

Kronecker coefficients: the tensor square conjecture and unimodality

Abstract : We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the $S_n$-irreducible representation indexed by the staircase partition contains every irreducible representation of $S_n$. We present a sufficient condition allowing to determine whether an irreducible representation is a constituent of a tensor square and using this result together with some analytic statements on partitions we prove Saxl conjecture for several partition classes. We also use Kronecker coefficients to give a new proof and a generalization of the unimodality of Gaussian ($q$-binomial) coefficients as polynomials in $q$, and extend this to strict unimodality.
Complete list of metadata

Cited literature [44 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Thursday, October 1, 2015 - 9:28:42 AM
Last modification on : Wednesday, August 7, 2019 - 12:14:40 PM
Long-term archiving on: : Saturday, January 2, 2016 - 10:50:23 AM


Publisher files allowed on an open archive




Igor Pak, Greta Panova, Ernesto Vallejo. Kronecker coefficients: the tensor square conjecture and unimodality. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.149-160, ⟨10.46298/dmtcs.2388⟩. ⟨hal-01207577⟩



Record views


Files downloads