Optimal Subgroups and Applications to Nilpotent Elements
| dc.creator | Bate, Michael | |
| dc.date | 2007-08-03 | |
| dc.date | 2008-05-12 | |
| dc.date.accessioned | 2026-07-07T09:37:53Z | |
| dc.date.available | 2026-07-07T09:37:53Z | |
| dc.description | Let G be a reductive group acting on an affine variety X, let x in X be a point whose G-orbit is not closed, and let S be a G-stable closed subvariety of X which meets the closure of the G-orbit of x but does not contain x. In this paper, we study G.R. Kempf's optimal class Omega_G(x,S) of cocharacters of G attached to the point x; in particular, we consider how this optimality transfers to subgroups of G. Suppose K is a G-completely reducible subgroup of G which fixes x, and let H = C_G(K)^0. Our main result says that the H-orbit of x is also not closed, and the optimal class Omega_H(x,S) for H simply consists of the cocharacters in Omega_G(x,S) which evaluate in H. We apply this result in the case that G acts on its Lie algebra via the adjoint representation to obtain some new information about cocharacters associated with nilpotent elements in good characteristic. | |
| dc.description | 11 pages, some minor changes | |
| dc.identifier | https://arxiv.org/abs/0708.0477 | |
| dc.identifier | http://arxiv.org/abs/0708.0477 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160618 | |
| dc.subject | Group Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 20G15, 14L24, 17B45 | |
| dc.title | Optimal Subgroups and Applications to Nilpotent Elements | |
| dc.type | text |