Kronecker coefficients: the tensor square conjecture and unimodality
Abstrak
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.
Topik & Kata Kunci
Penulis (3)
Igor Pak
Greta Panova
Ernesto Vallejo
Akses Cepat
- Tahun Terbit
- 2014
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2388
- Akses
- Open Access ✓