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

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

2008-12-04

arxiv.org/abs/0812.0861v1

Mathematics

Combinatorics

12 pages. See also http://emmanuel.jean.briand.free.fr/publications/

Scientific paper

We show that the Kronecker coefficients (the Clebsch-Gordan coefficients of the symmetric group) 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.

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