Spaltenstein varieties of pure dimension

Yiqiang Li

doi:10.1090/proc/14726

Spaltenstein varieties of pure dimension

Yiqiang Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that Spaltenstein varieties of classical groups are pure dimensional when the Jordan-type of the nilpotent element involved is an even or odd partition. We further show that they are Lagrangian in the partial resolutions of the associated nilpotent Slodowy slices, from which their dimensions are known to be one half of the dimension of the partial resolution minus the dimension of the nilpotent orbit. The results are then extended to the σ-quiver-variety setting.

Original language	English
Pages (from-to)	133-144
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	1
DOIs	https://doi.org/10.1090/proc/14726
State	Published - 2020

Keywords

C-action
Nilpotent Slodowy slices of classical groups
Pure dimensionality
Spaltenstein varieties
Symplectic geometry
σ-quiver varieties

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10.1090/proc/14726

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abstract = "We show that Spaltenstein varieties of classical groups are pure dimensional when the Jordan-type of the nilpotent element involved is an even or odd partition. We further show that they are Lagrangian in the partial resolutions of the associated nilpotent Slodowy slices, from which their dimensions are known to be one half of the dimension of the partial resolution minus the dimension of the nilpotent orbit. The results are then extended to the σ-quiver-variety setting.",

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AB - We show that Spaltenstein varieties of classical groups are pure dimensional when the Jordan-type of the nilpotent element involved is an even or odd partition. We further show that they are Lagrangian in the partial resolutions of the associated nilpotent Slodowy slices, from which their dimensions are known to be one half of the dimension of the partial resolution minus the dimension of the nilpotent orbit. The results are then extended to the σ-quiver-variety setting.

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KW - Nilpotent Slodowy slices of classical groups

KW - Pure dimensionality

KW - Spaltenstein varieties

KW - Symplectic geometry

KW - σ-quiver varieties

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JF - Proceedings of the American Mathematical Society

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Spaltenstein varieties of pure dimension

Abstract

Keywords

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