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math.AG2005
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.…
math.AG2003
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…
math.AG2003★ 5 cited
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…