5 citations · 6 across the 6 of their papers we have counts for
9 papers
The algebra of Mirkovic-Vilonen cycles in type A
Jared E. Anderson, Mikhail Kogan
Let Gr be the affine Grassmannian for a connected complex reductive group G. Let C_G be the complex vector space spanned by (equivalence classes of) Mirkovic-Vilonen cycles in Gr.…
Localization theorems by symplectic cuts
Lisa Jeffrey, Mikhail Kogan
Given a compact symplectic manifold M with the Hamiltonian action of a torus T, let zero be a regular value of the moment map, and M_0 the symplectic reduction at zero. Denote by κ…
Morse theory on Hamiltonian G-spaces and equivariant K-theory
Victor Guillemin, Mikhail Kogan
Let be a torus and a compact Hamiltonian -manifold with finite fixed point set . If is a circle subgroup of with , the -moment map is a Morse fu…
Mirkovic-Vilonen cycles and polytopes in type A
Jared E. Anderson, Mikhail Kogan
We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirković and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that…
Toric degeneration of Schubert varieties and Gel'fand-Cetlin polytopes
Mikhail Kogan, Ezra Miller
This note constructs the flat toric degeneration of the manifold FL_n of flags in C^n from [Gonciulea-Lakshmibai 96] as an explicit GIT quotient of the Gr"obner degeneration in [Kn…
Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles
Mikhail Kogan
Given an rc-graph of permutation and an rc-graph of permutation , we provide an insertion algorithm, which defines an rc-graph in the case when i…