Torus quotients of homogeneous spaces-minimal dimensional Schubert Variety admitting semi-stable points

2008/07/30 by Kannan, S. S., Pattanayak, S. K. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0807.4818

Abstract

In this paper, for any simple, simply connected algebraic group G of type B_n,C_n or D_n and for any maximal parabolic subgroup P of G, we describe all minimal dimensional Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. In this paper, we also describe, for any semi-simple simply connected algebraic group G and for any Borel subgroup B of G, all Coxeter elements τ for which the Schubert variety X(τ) admits a semistable point for the action of the torus T with respect to a non-trivial line bundle on G/B.

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