Upper cluster structure on Kac--Moody Richardson varieties

Fuente: arXiv
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Main Authors: Bao, Huanchen, Ye, Jeff York
Format: Preprint
Published: 2025
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_version_ 1866915434175922176
author Bao, Huanchen
Ye, Jeff York
author_facet Bao, Huanchen
Ye, Jeff York
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_10382
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Upper cluster structure on Kac--Moody Richardson varieties
Bao, Huanchen
Ye, Jeff York
Representation Theory
Algebraic Geometry
Combinatorics
13F60, 14M15, 20G44
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.
title Upper cluster structure on Kac--Moody Richardson varieties
topic Representation Theory
Algebraic Geometry
Combinatorics
13F60, 14M15, 20G44
url https://arxiv.org/abs/2506.10382