2005/01/26 by Ketan Mulmuley, Ketan D. Mulmuley, Mulmuley, Ketan D. +3 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Computational Complexity (cs.CC) #F1.3 #FOS: Computer and information sciences #FOS: Mathematics #Representation Theory (math.RT) #cs.CC #math.RT
paper · pdf · doi:10.48550/arxiv.cs/0501076
10 pages
arxiv created 2005/01/26 · openalex publication_date 2005/01/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.