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arXiv · 2506.10382

Upper cluster structure on Kac--Moody Richardson varieties

Huanchen Bao·Jeff York Ye
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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.

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Huanchen Bao, Jeff York Ye. 2025-06-12. Upper cluster structure on Kac--Moody Richardson varieties. https://arxiv.org/abs/2506.10382

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