3 citations · 11 across the 6 of their papers we have counts for
10 papers
Relation between two geometrically defined bases in representations of
Alexander Braverman, Dennis Gaitsgory, Maxim Vybornov
Let be an irreducible representation of group , which appears as a submodule in , where is the tautological -…
Quiver varieties and Lusztig's algebra
Anton Malkin, Victor Ostrik, Maxim Vybornov
We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL(2). As an application, ADE quiver varieties of Nakajima are…
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…
Quiver varieties, affine Lie algebras, algebras of BPS states, and semicanonical basis
Igor Frenkel, Anton Malkin, Maxim Vybornov
We suggest a (conjectural) construction of a basis in the plus part of the affine Lie algebra of type ADE indexed by irreducible components of certain quiver varieties. This constr…