Lattice associated to a Shi variety

Abstract

Let W be an irreducible Weyl group and W a its affine Weyl group. In [4] the author defined an affine variety (cid:2) X W a , called the Shi variety of W a , whose integral points are in bijection with W a . The set of irreducible components of (cid:2) X W a , denoted H 0 ( (cid:2) X W a ), is of some interest and we show in this article that H 0 ( (cid:2) X W a ) has a structure of a semidistributive lattice.