Lattice associated to a Shi variety
Abstract
Let W be a irreducible Weyl group and Wa its affine Weyl group. In a previous article the author defined an affine variety XWa, called the Shi variety of Wa, whose integral points are in bijection with Wa. The set of irreducible components of XWa, denoted H0(XWa), is of some interest and we show in this article that H0(XWa) has a structure of semidistributive lattice.
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