2019/10/12 by Goldring, Wushi
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1910.05618
In joint work with J.-S. Koskivirta, we had previously introduced the notion of "quasi-constant" character (of a maximal torus of a connected reductive group over a field); we showed that over an algebraically closed field it naturally unifies the notions "minuscule" and "co-minuscule". In this note we describe a characterization of quasi-constant fundamental weights in terms of the Weyl group of a maximal Levi subgroup. Equivalently, purely in the language of root systems, the result characterizes special and co-special vertices of Dynkin diagrams in terms of Weyl groups of maximal sub-root systems.