The Geometry of Fixed Point Varieties on Affine Flag Manifolds
| dc.creator | Sage, Daniel S. | |
| dc.date | 1999-01-22 | |
| dc.date.accessioned | 2026-07-07T05:27:38Z | |
| dc.date.available | 2026-07-07T05:27:38Z | |
| dc.description | Let $G$ be a semisimple, simply connected, algebraic group over an algebraically closed field $k$ with Lie algebra $\frak g$. We study the spaces of parahoric subalgebras of a given type containing a fixed nil-elliptic element of $\frak g\otimes k((π))$, i.e. fixed point varieties on affine flag manifolds. We define a natural class of $k^*$-actions on affine flag manifolds, generalizing actions introduced by Lusztig and Smelt. We formulate a condition on a pair $(N,f)$ consisting of $N\in\frak{g}\otimes k((π))$ and a $k^*$-action $f$ of the specified type which guarantees that $f$ induces an action on the variety of parahoric subalgebras containing $N$. For the special linear and symplectic groups, we characterize all regular semisimple and nil-elliptic conjugacy classes containing a representative whose fixed point variety admits such an action. We then use these actions to find simple formulas for the Euler characteristics of those varieties for which the $k^*$-fixed points are finite. We also obtain a combinatorial description of the Euler characteristics of the spaces of parabolic subalgebras containing a given element of certain nilpotent conjugacy classes of $\frak g$. | |
| dc.description | Latex2e, 33 pages. To appear in Transactions of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/9901097 | |
| dc.identifier | http://arxiv.org/abs/math/9901097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77989 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L30; 20G25 | |
| dc.title | The Geometry of Fixed Point Varieties on Affine Flag Manifolds | |
| dc.type | text |