Chimney retractions in affine buildings encode orbits in affine flag varieties

Document Type

Journal Article

Role

Author

Publisher

Mathematical Sciences Publishers

Availability

Check Tripod

Journal Title

Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial

Volume

20

Issue

2-3

First Page

395

Last Page

430

Publication Date

9-13-2023

Abstract

This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides a unified framework to study orbits in affine flag varieties. We introduce the notion of labeled folded galleries for any affine building X and use these to describe the preimages of chimney retractions. When X is the building for a group with an affine Tits system, such as the Bruhat–Tits building for a group over a local field, we can then relate labeled folded galleries and shadows to double coset intersections in affine flag varieties. This result generalizes the authors’ previous joint work with Naqvi on groups over function fields.

Comments

Preprint version available at https://doi.org/10.48550/arXiv.2207.12923

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