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

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

2005-01-26

arxiv.org/abs/cs/0501076v1

Computer Science

Computational Complexity

10 pages

Scientific paper

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.

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