Equivariant geometry of symmetric quiver orbit closures

Ryan Kinser; Martina Lanini; Jenna Rajchgot

doi:10.48550/arxiv.2410.06929

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Equivariant geometry of symmetric quiver orbit closures

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Equivariant geometry of symmetric quiver orbit closures

Ryan Kinser, Martina Lanini and Jenna Rajchgot

ArXiv.org

Cornell University

10/09/2024

DOI: 10.48550/arxiv.2410.06929

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https://doi.org/10.48550/arxiv.2410.06929View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties GL(n)/K where K is an orthogonal or symplectic group. In particular, we translate results about singularities of orbit closures; combinatorics of orbit closure containment; and torus equivariant cohomology and K-theory between these classes of varieties. We obtain these results by constructing explicit embeddings with nice properties of homogeneous fiber bundles over type A symmetric quiver representation varieties into symmetric varieties.

Mathematics - Algebraic Geometry

Mathematics - Combinatorics

Mathematics - Representation Theory

Details

Title: Subtitle: Equivariant geometry of symmetric quiver orbit closures
Creators: Ryan Kinser
Martina Lanini
Jenna Rajchgot
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2410.06929
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 10/09/2024
Academic Unit: Mathematics
Record Identifier: 9984722574202771

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