192 citations · 390 across the 13 of their papers we have counts for
13 papers
Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds
Eugene Lerman, Anton Malkin
We develop differential and symplectic geometry of differentiable Deligne-Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application…
Equivariant differential characters and symplectic reduction
Eugene Lerman, Anton Malkin
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction.
Differential characters as stacks and prequantization
Eugene Lerman, Anton Malkin
We generalize geometric prequantization of symplectic manifolds to differentiable stacks. Our approach is atlas-independent and provides a bijection between isomorphism classes of…
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…
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…
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…