Laumon parahoric local models via quiver Grassmannians

Evgeny Feigin, Martina Lanini*, Alexander Pütz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers are quiver Grassmannians for the loop quiver and the special fiber is a certain quiver Grassmannian for the cyclic quiver. The whole family sits inside the Gaitsgory central degeneration of the affine Grassmannians. We study the properties of the special fibers of the (complex) Laumon local models for arbitrary parahoric subgroups in type A using the machinery of quiver representations. We describe the irreducible components and the natural strata with respect to the group action for the quiver Grassmannians in question. We also construct a cellular decomposition and provide an explicit description for the corresponding poset of cells. Finally, we study the properties of the desingularizations of the irreducible components and show that the desingularization construction is compatible with the natural projections between the parahoric subgroups.

Original languageEnglish
Article number107837
JournalJournal of Pure and Applied Algebra
Volume229
Issue number1
DOIs
StatePublished - Jan 2025

Funding

FundersFunder number
Ministero dell’Istruzione, dell’Università e della Ricerca
Deutsche ForschungsgemeinschaftSFB-TRR 358/1 2023 — 491392403
Israel Science FoundationPRIN2022 CUP E53D23005550006, CUP E83C18000100006, 2023–2027

    Keywords

    • Affine flag varieties
    • Local models of Shimura varieties
    • Quiver Grassmannians

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