Combinatorics in affine flag varieties

Details Combinatorics in affine flag varieties Combinatorics in affine flag varieties

2008-01-04

arxiv.org/abs/0801.0709v1

Mathematics

Representation Theory

21 pages,

Scientific paper

The Littelmann path moel gives a realization of the crystals of integrable representations of symmetrizable Kac-Moody Lie algebras. Recent work of Gaussent-Littelmann and others has demonstrated a connection between this model and the geometry of the loop Grassmannian. The alcove walk model is a version of the path model which is intimately connected to the combinatorics of the affine Hecke algebra. In this paper we define a refined alcove walk model which encodes the points of the affine flag variety. We show that this combinatorial indexing naturally indexes the "cells" in generalized Mirkovic-Vilonen intersections.

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