2020/04/21 by Marc Besson, Besson, Marc, Sam Jeralds +3
Mathematics · #22E46 (Primary) 05E10 #52A40 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2004.09711
openalex publication_date 2020/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscrK(G) be the rational cone generated by pairs (λ, μ) where λ and μ are dominant integral weights and μ is a nontrivial weight space in the representation Vλ of G. We produce all extremal rays of \mathscrK(G) by considering the vertices of corresponding intersection polytopes IPλ, the set of points in \mathscrK(G) with first coordinate λ. We show that vertices of IP\varpii arise as lifts of vertices coming from cones \mathscrK(L) associated to simple Levi subgroups possessing the simple root αi. As corollaries we obtain a complete description of all extremal rays, as well as polynomial formulas describing the numbers of extremal rays depending on type and rank.