Wilson's grassmannian and a noncommutative Quadric
| dc.creator | Baranovsky, Vladimir | |
| dc.creator | Ginzburg, Victor | |
| dc.creator | Kuznetsov, Alexander | |
| dc.date | 2002-03-13 | |
| dc.date | 2002-10-27 | |
| dc.date.accessioned | 2026-07-07T04:47:00Z | |
| dc.date.available | 2026-07-07T04:47:00Z | |
| dc.description | Let the group G of m-th roots of unity act on the complex line by multiplication, inducing an action on the algebra, Diff, of polynomial differential operators on the line. Following Crawley-Boevey and Holland, we introduce a multiparameter deformation, D_c, of the smash-product (Diff # G). Our main result provides natural bijections between (roughly speaking) the following spaces: (1) G-equivariant version of Wilson's adelic Grassmannian of rank r; (2) Rank r projective D_c-modules (equipped with generic trivialization); (3) Rank r torsion-free sheaves on a `noncommutative quadric'; (4) Disjoint union of Nakajima quiver varieties for the cyclic quiver with m vertices. The bijection between (1) and (2) is provided by a version of Riemann-Hilbert correspondence between D-modules and sheaves. The bijections between (2), (3) and (4) were motivated by our previous work math.AG/0103068. The resulting bijection between (1) and (4) reduces, in the very special case: r=1 and G=1, to the partition of (rank 1) adelic Grassmannian into a union of Calogero-Moser spaces, discovered by Wilson. This gives, in particular, a natural and purely algebraic approach to Wilson's result. | |
| dc.description | 35pp, several remarks, and an open problem (at the end of the Introduction) added | |
| dc.identifier | https://arxiv.org/abs/math/0203116 | |
| dc.identifier | http://arxiv.org/abs/math/0203116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63548 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Quantum Algebra | |
| dc.title | Wilson's grassmannian and a noncommutative Quadric | |
| dc.type | text |