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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.