Type D quiver representation varieties, double Grassmannians, and symmetric varieties

We unify aspects of the equivariant geometry of type $D$ quiver representation varieties, double Grassmannians, and symmetric varieties $GL(a+b)/GL(a)\times GL(b)$; in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivar...

Full description

Saved in:
Bibliographic Details
Main Authors Kinser, Ryan, Rajchgot, Jenna
Format Journal Article
LanguageEnglish
Published 28.01.2019
Subjects
Mathematics - Algebraic Geometry
Mathematics - Representation Theory
Online AccessGet full text

Cover

More Information
Summary:We unify aspects of the equivariant geometry of type $D$ quiver representation varieties, double Grassmannians, and symmetric varieties $GL(a+b)/GL(a)\times GL(b)$; in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant $K$-theory between these three families. These results are all obtained from our generalization of a construction of Zelevinsky for type $A$ quivers to the type $D$ setting. More precisely, we give explicit embeddings with nice properties of homogeneous fiber bundles over type $D$ quiver representation varieties into these symmetric varieties.
DOI:10.48550/arxiv.1901.10014