Quasipolynomial formulas for the Kronecker coefficients indexed by two two-row shapes (extended abstract)

Description

We show that the Kronecker coefficients indexed by two two–row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. These new formulas are obtained from analogous formulas for the corresponding reduced Kronecker coefficients and a formula recovering the Kronecker coefficients from the reduced Kronecker coefficients. As an application, we characterize all the Kronecker coefficients indexed by two two-row shapes that are equal to zero. This allowed us to disprove a conjecture of Mulmuley about the behavior of the stretching functions attached to the Kronecker coefficients.

Abstract

Ministerio de Educación y Ciencia MTM2007–64509

Abstract

Junta de Andalucía FQM–333

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