2024/07/22 by Gong, Tao
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2407.16070
Given a reduced crystallographic root system with a fixed simple system, it is associated to a Weyl group W, parabolic subgroups WK's and a polytope P which is the convex hull of a dominant weight. The quotient P/WK can be identified with a polytope. Polytopes P and P/WK are associated to toric varieties XP and XP/WK respectively. It turns out the underlying topological spaces XP/WK and XP/WK are homotopy equivalent, when considering the polytopes in the real span of the root lattice or of the weight lattice.