Cyclic Demazure Modules and Positroid Varieties

Abstract

A positroid variety is an intersection of cyclically rotated Grassmannian Schubert varieties.  Each graded piece of the homogeneous coordinate ring of a positroid variety is the intersection of cyclically rotated (rectangular) Demazure modules, which we call the cyclic Demazure module.  In this note, we show that the cyclic Demazure module has a canonical basis, and define the cyclic Demazure crystal.