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arXiv · 1912.09911

A gallery model for affine flag varieties via chimney retractions

Elizabeth Milićević·Yusra Naqvi·Petra Schwer·Anne Thomas
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Abstract

This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat-Tits buildings. We first formulate, for arbitrary affine buildings, the notion of a chimney retraction. This simultaneously generalizes 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 in the function field case, we relate these retractions and their effect on minimal galleries to double coset intersections in the corresponding affine flag variety.

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Elizabeth Milićević, Yusra Naqvi, Petra Schwer, Anne Thomas. 2022-04-07. A gallery model for affine flag varieties via chimney retractions. https://arxiv.org/abs/1912.09911

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