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 that are related to the geometric classification of certain 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 (based on arXiv 2504.08717). Time permitting, we will also discuss the deformations of these singular Lagrangian subvarieties.
This is a Zoom talk streamed in Huxley, so you can participate online or attend in person.