Convex Polytopes for the Central Degeneration of the Affine Grassmannian
Abstract
We study the algebraic geometry and combinatorics of the central degeneration (the degeneration that shows up in local models of Shimura varieties and Gaitsgory's central sheaves) in type A. More specifically, we elucidate the central degeneration of semiinfinite orbits and explain its relations with Levi restriction. Also, we discuss the central degeneration of Mirkovi$\acute{\text{c}}$Vilonen cycles in the affine Grassmannian, and the corresponding transformations of Mirkovi$\acute{\text{c}}$Vilonen polytopes. In addition, we shed some light on the geometry of Iwahori MV cycles in the affine Grassmannian and generalized MV cycles in the affine flag variety, which are closely related to Demazure modules and affine DeligneLusztig varieties respectively.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.08641
 Bibcode:
 2016arXiv160408641Z
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory
 EPrint:
 Keywords: Affine Grassmannian