Abstract
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the toroidal and horospherical partial flag varieties with Picard number 1. In the more general case, we provide a set of necessary conditions for the action of a Levi subgroup on a Schubert variety to be toroidal. The singular locus of a (co)minuscule Schubert variety is shown to contain all the Lmax-stable Schubert subvarieties, where Lmax is the standard Levi subgroup of the maximal parabolic which acts on the Schubert variety by left multiplication. In type A, the effect of the Billey-Postnikov decomposition on toroidal Schubert varieties is obtained.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
