A gallery model for affine flag varieties via chimney retractions

Abstract: A gallery model for affine flag varieties via chimney retractions We provide a unified combinatorial framework to study orbits in affine flag varieties via the associated Bruhat-Tits buildings. We first formulate, for arbitrary affine buildings, the notion of a chimney retraction. This simultaneously generalises the two well-known notions of retractions in affine buildings: retractions from chambers at infinity and retractions from alcoves. We then present a recursive formula for computing the images of certain minimal galleries in the building under chimney retractions, using purely combinatorial tools associated to the underlying affine Weyl group. Finally, for Bruhat-Tits buildings, we relate these retractions and their effect on certain minimal galleries to double coset intersections in the corresponding affine flag variety. This is joint work with Elizabeth Milicevic, Yusra Naqvi and Petra Schwer.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle