2022/10/11 by Sam Jeralds, Jeralds, Sam, Shrawan Kumar +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2210.05473
Kostant asked the following question: Let \mathfrakg be a simple Lie algebra over the complex numbers. Let λ be a dominant integral weight. Then, V(λ) is a component of V(ρ)⊗ V(ρ) if and only if λ≤ 2 ρ under the usual Bruhat-Chevalley order on the set of weights. In an earlier work with R. Chirivi and A. Maffei the second author gave an affirmative answer to this question up to a saturation factor. The aim of the current work is to extend this result to untwisted affine Kac-Moody Lie algebra \mathfrakg associated to any simple Lie algebra \mathring\mathfrakg (up to a saturation factor). In fact, we prove the result for affine sln without any saturation factor. Our proof requires some additional techniques including the Goddard-Kent-Olive construction and study of the characteristic cone of non-compact polyhedra.