Affine Demazure modules and $T$-fixed point subschemes in the affine Grassmannian
| dc.creator | Zhu, Xinwen | |
| dc.date | 2007-10-27 | |
| dc.date | 2008-11-20 | |
| dc.date.accessioned | 2026-07-07T10:19:17Z | |
| dc.date.available | 2026-07-07T10:19:17Z | |
| dc.description | Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $λ$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^λ)^T$ of the Schubert variety $\bar{Gr}_G^λ$ in the affine Grassmannian $Gr_G$ is a finite scheme. We prove that there is a natural isomorphism between the dual of the level one affine Demazure module corresponding to $λ$ and the ring of functions (twisted by certain line bundle on $Gr_G$) of $(\bar{Gr}_G^λ)^T$. We use this fact to give a geometric proof of the Frenkel-Kac-Segal isomorphism between basic representations of affine algebras of $A,D,E$ type and lattice vertex algebras. | |
| dc.description | 25 pages, | |
| dc.identifier | https://arxiv.org/abs/0710.5247 | |
| dc.identifier | http://arxiv.org/abs/0710.5247 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174455 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M15; 17B69 | |
| dc.title | Affine Demazure modules and $T$-fixed point subschemes in the affine Grassmannian | |
| dc.type | text |