Kronecker coefficients: The tensor square conjecture and unimodality
Por:
Pak I., Panova G., Vallejo E.
Publicada:
1 ene 2014
Resumen:
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 Sn-irreducible representation indexed by the staircase partition contains every irreducible representation of Sn. 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. © 2014 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France
Filiaciones:
Pak I.:
University of California, Los Angeles, United States
Panova G.:
University of California, Los Angeles, United States
Vallejo E.:
Centro de Ciencias Matemáticas, Universidad Nacionál Autónoma de México, Morelia, Mexico
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