2019/09/19 by Kiers, Joshua
#14C17 #14M15 #15A42 #22E46 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1909.09262
We examine the extremal rays of the cone of dominant weights (μ, \widehatμ) for groups G⊆ \widehat G for which there exists N ≫0 such that (V(Nμ)⊗ V(N\widehat μ))G≠ (0). We exhibit formulas for a class of rays ("type I") on any regular face of the cone. These rays are identified thanks to a generalization of Fulton's conjecture, which we prove along the way. We verify that the remaining rays ("type II") on the face are the images of extremal rays for a smaller cone under a certain map, whose formula is given. A procedure is given for finding the rays of the cone not on any regular face. This is a generalization of the work of Belkale and Kiers on extremal rays for the saturated tensor cone; the specialization is given by \widehat G = G× G with the diagonal embedding of G. We include several examples to illustrate the formulas.