Minimal Parabolic subgroups and Automorphism groups of Schubert varieties-II

2022/09/26 by Kannan, S. Senthamarai, Saha, Pinakinath
#14M15 #14M17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2209.12838

Abstract

Let G be a simple algebraic group of adjoint type over the field ℂ of complex numbers, B be a Borel subgroup of G containing a maximal torus T of G. In this article, we show that α is a co-minuscule root if and only if for any parabolic subgroup Q containing B properly, there is no Schubert variety X_Q(w) in G/Q such that the minimal parabolic subgroup P_α of G is the connected component, containing the identity automorphism of the group of all algebraic automorphisms of X_Q(w).

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