The algebra of Mirkovic-Vilonen cycles in type A
| dc.creator | Anderson, Jared E. | |
| dc.creator | Kogan, Mikhail | |
| dc.date | 2005-05-06 | |
| dc.date.accessioned | 2026-07-07T05:19:40Z | |
| dc.date.available | 2026-07-07T05:19:40Z | |
| dc.description | 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. The Beilinson-Drinfeld Grassmannian can be used to define a convolution product on MV-cycles, making C_G into a commutative algebra. We show, in type A, that C_G isomorphic to C[N], the algebra of functions on the unipotent radical N of a Borel subgroup of G; then each MV-cycle defines a polynomial in C[N], which we call an MV-polynomial. We conjecture that those MV-polynomials which are cluster monomials for a Fomin-Zelevinsky cluster algebra structure on C[N] are naturally expressible as determinants, and we conjecture a formula for many of them. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505100 | |
| dc.identifier | http://arxiv.org/abs/math/0505100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75100 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 14L35 | |
| dc.title | The algebra of Mirkovic-Vilonen cycles in type A | |
| dc.type | text |