Minimal parabolic subgroups and automorphism groups of Schubert varieties

2022/09/20 by S. Kannan, Kannan, S. Senthamarai, Pinakinath Saha +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2209.09748

Abstract

Let G be a simple simply-laced 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 ω_α is a minuscule fundamental weight 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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