Geometric Complexity III: on deciding positivity of Littlewood-Richardson coefficients

Abstract

We point out that the remarkable Knutson and Tao Saturation Theorem and polynomial time algorithms for LP have together an important and immediate consequence in Geometric Complexity Theory. The problem of deciding positivity of Littlewood-Richardson coefficients for GLn(C) belongs to P. Furthermore, the algorithm is strongly polynomial. The main goal of this article is to explain the significance of this result in the context of Geometric Complexity Theory. Furthermore, it is also conjectured that an analogous result holds for arbitrary symmetrizable Kac-Moody algebras.

arXiv comment10 pages

References in corpus (2)

• Honeycombs and sums of Hermitian matrices
• Littlewood-Richardson semigroups

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• Reduced Kronecker coefficients and counter-examples to Mulmuley's strong saturation conjecture SH
• Geometric Complexity Theory V: On deciding nonvanishing of a generalized Littlewood-Richardson coefficient