Geometric construction of metaplectic covers of $\GL_{n}$ in characteristic zero
| dc.creator | Hill, Richard | |
| dc.date | 2007-08-01 | |
| dc.date.accessioned | 2026-07-07T08:21:42Z | |
| dc.date.available | 2026-07-07T08:21:42Z | |
| dc.description | This paper presents a new construction of the m-fold metaplectic cover of $\GL_{n}$ over an algebraic number field k, where k contains a primitive m-th root of unity. A 2-cocycle on $\GL_{n}(\A)$ representing this extension is given and the splitting of the cocycle on $\GL_{n}(k)$ is found explicitly. The cocycle is smooth at almost all places of k. As a consequence, a formula for the Kubota symbol on $\SL_{n}$ is obtained. The construction of the paper requires neither class field theory nor algebraic K-theory, but relies instead on naive techniques from the geometry of numbers introduced by W. Habicht and T. Kubota. The power reciprocity law for a number field is obtained as a corollary. | |
| dc.description | 90 pages | |
| dc.identifier | https://arxiv.org/abs/0708.0108 | |
| dc.identifier | http://arxiv.org/abs/0708.0108 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135407 | |
| dc.subject | Number Theory | |
| dc.subject | 11F99 | |
| dc.title | Geometric construction of metaplectic covers of $\GL_{n}$ in characteristic zero | |
| dc.type | text |