Dimensions of some affine Deligne-Lusztig varieties
| dc.creator | Goertz, Ulrich | |
| dc.creator | Haines, Thomas J. | |
| dc.creator | Kottwitz, Robert E. | |
| dc.creator | Reuman, Daniel C. | |
| dc.date | 2005-04-22 | |
| dc.date.accessioned | 2026-07-07T05:19:19Z | |
| dc.date.available | 2026-07-07T05:19:19Z | |
| dc.description | This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties X_mu(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of superbasic b. In the affine flag manifold, we prove a formula that reduces the dimension question for X_x(b) with b in the split torus to computations of dimensions of intersections of Iwahori orbits with orbits of the unipotent radical. Calculations using this formula allow us to verify a conjecture of Reuman in many new cases, and to make progress toward a generalization of his conjecture. | |
| dc.description | 51 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/math/0504443 | |
| dc.identifier | http://arxiv.org/abs/math/0504443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74979 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 14L05 (Primary) 11S25, 20G25, 14F30 (Secondary) | |
| dc.title | Dimensions of some affine Deligne-Lusztig varieties | |
| dc.type | text |