Upper cluster structure on Kac--Moody Richardson varieties
Representation Theory
2025-08-11 v2 Algebraic Geometry
Combinatorics
Abstract
We show coordinate rings of open Richardson varieties are upper cluster algebras for any symmetrizable Kac--Moody type. We further show the coordinate rings of (generalized) open Richardson varieties on the twisted product of flag varieties are upper cluster algebras for any symmetrizable Kac--Moody type. This includes, as special cases, reduced double Bruhat cells, Bott-Samelson varieties, braid varieties. Our results generalize various results by Casals--Gorsky--Gorsky--Le--Shen--Simental and Galashin--Lam--Sherman-Bennett--Speyer in finite types.
Keywords
Cite
@article{arxiv.2506.10382,
title = {Upper cluster structure on Kac--Moody Richardson varieties},
author = {Huanchen Bao and Jeff York Ye},
journal= {arXiv preprint arXiv:2506.10382},
year = {2025}
}
Comments
v2, 30 pages. We updated the references and made various minor updates