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Posted April 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Mengwei Hu, Yale University
On certain Lagrangian subvarieties in minimal resolutions of Kleinian singularities

Kleinian singularities are quotients of C^2 by finite subgroups of SL_2(C). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities, motivated by the geometric classification of unipotent Harish-Chandra (g,K)-modules. The irreducible components of these singular Lagrangian subvarieties are P^1's and A^1's. I will describe how they intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties. I will also discuss their connections with nilpotent K-orbits and symmetric pairs in semisimple Lie algebras.