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Perverse sheaves, Koszul IC-modules, and the quiver for the category O
Maxim Vybornov
For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d^2=0. We prove that the c…
The minimal degeneration singularities in the affine Grassmannians
Anton Malkin, Viktor Ostrik, Maxim Vybornov
The minimal degeneration singularities in the affine Grassmannians of simple simply-laced algebraic groups are determined to be either Kleinian singularities of type A, or closures…
On quiver varieties and affine Grassmannians of type A
Ivan Mirković, Maxim Vybornov
We construct Nakajima's quiver varieties of type A in terms of affine Grassmannians of type A. This gives a compactification of quiver varieties and a decomposition of affine Grass…
Constructible sheaves on simplicial complexes and Koszul duality
Maxim Vybornov
We obtain a linear algebra data presentation of the category of constructible with respect to perverse triangulation sheaves on a finite simplicial complex. We also establish Koszu…