Matsuki duality for loop groups
Representation Theory
2026-04-23 v2 Algebraic Geometry
Number Theory
Abstract
We establish versions of Matsuki duality for loop groups. The main result is a bijection between symmetric loop group orbits and real polynomial loop group orbits on the affine Grassmannians or affine flag varieties. Along the way we obtain orbit parametrizations and make connections with vector bundles on real and twistor- and Kottwitz sets .
Keywords
Cite
@article{arxiv.2604.15712,
title = {Matsuki duality for loop groups},
author = {Tsao-Hsien Chen and Lingfei Yi},
journal= {arXiv preprint arXiv:2604.15712},
year = {2026}
}
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31 pages