Milićević, Elizabeth;
Naqvi, Yusra;
Schwer, Petra;
Thomas, Anne;
(2022)
A Gallery Model for Affine Flag Varieties via Chimney Retractions.
Transformation Groups
10.1007/s00031-022-09726-8.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | A Gallery Model for Affine Flag Varieties via Chimney Retractions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00031-022-09726-8 |
| Publisher version: | https://doi.org/10.1007/s00031-022-09726-8 |
| Language: | English |
| Additional information: | © 2022 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10150458 |
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