On Certain Lagrangian Subvarieties in Minimal Resolutions of Kleinian Singularities

Mon Jan 27, 2025 4:30 p.m.—5:30 p.m.
Exterior of Sheffield-Sterling-Strathcona Hall featuring a stone carving of Yale's coat of arms and motto

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Seminar: 
Geometry, Symmetry and Physics

Event time: 
Monday, January 27, 2025 - 4:30pm

Location: 
KT 801

Speaker: 
Mengwei Hu

Speaker affiliation: 
Yale

Event description: 
Kleinian singularities are remarkable singular affine surfaces. They arise as quotients of C^2 by finite subgroups of SL_2(C). The exceptional loci in the minimal resolutions of Kleinian singularities are in 1-to-1 correspondence with simply-laced Dynkin diagrams. In this talk, I will introduce certain singular Lagrangian subvarieties in minimal resolutions of Kleinian singularities that appear in the classification of irreducible Harish-Chandra (g, K)-modules. These singular Lagrangian subvarieties have irreducible components given by P^1’s and A^1’s and contain the exceptional locus as a subvariety. I will describe how these irreducible components intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties.

Research Area(s): 
Algebraic Geometry
Representation Theory