An analogue of Bott's theorem for Schubert varieties-related to torus semistable points

2012/12/27 by Kannan, S. Senthamarai
#14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1212.6338

Abstract

Let G be a simple, simply connected algebraic group over the field of complex numbers. We give a necessary and a sufficient condition for a Schubert variety X(τ) for which all the higher cohomologies Hⁱ(X(τ), E) vanish for the restriction E of the tangent bundle of G/B to X(τ). We further show that the global sections H⁰(X(τ), E) is the adjoint representation of G when G is simply laced.

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