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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.AG2001
A polytope combinatorics for semisimple groups
Jared E. Anderson
Mirkovic and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images…