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

 

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Opened Access Quasipolynomial formulas for the Kronecker coefficients indexed by two two-row shapes (extended abstract)
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Author: Briand, Emmanuel
Orellana, Rosa
Rosas Celis, Mercedes Helena
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Universidad de Sevilla. Departamento de álgebra
Date: 2008
Published in: ArXiv.org, arXiv:0812.0861
Document type: Article
Abstract: 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.
Cite: Briand, E., Orellana, R. y Rosas Celis, M.H. (2008). Quasipolynomial formulas for the Kronecker coefficients indexed by two two-row shapes (extended abstract). ArXiv.org, arXiv:0812.0861
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URI: https://hdl.handle.net/11441/87787

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