Representación de weil del grupo sl*(2,fq[x]/[xm]).
Let A be a unitary ring with invohition *. The groups SL(2. A) were defined by J. Pantoja and J. Soto Andrade in 141. These groups are a noncomnutative version of the special linear groups SL(2 F) defined over a commutative base fleid F. In particular, if A is (he fuli rnatrix ring M(2, F) endowed w...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | Chile |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.anid.cl:10533/179405 |
| Acceso en línea: | http://creativecommons.org/licenses/by-nc-nd/3.0/cl/ https://hdl.handle.net/10533/179405 |
| Access Level: | acceso abierto |
| Sumario: | Let A be a unitary ring with invohition *. The groups SL(2. A) were defined by J. Pantoja and J. Soto Andrade in 141. These groups are a noncomnutative version of the special linear groups SL(2 F) defined over a commutative base fleid F. In particular, if A is (he fuli rnatrix ring M(2, F) endowed with the trasposition as irivolution. then SL,(2, A) coincides with thc syinplectic group Sp(2n, F) in 2n variables. In (bis thesis we study the truncated poliiioniial rings Am Fq / Xm)) with k a finite fleid of odd cliaracteritic p, for any positive integer rn endowed with the natural involution givdn x —x. Thcsc rings, reminiscent of algebras de m-jets, appear when rn is a power of p, with a different involut,ion as polinoinial modeis for Ihe non- semi-simple rno(lular group algcl)ras k [( ,] oer a base fleid of charactensi i(: p, whose itivolutioii is given liv inversioli iii (he group. Wc obtain a fuil cliaractcrizatioii of all the involutions in the ring for any m and the fact tliat t.herc is only one isoniorphisrn type of non trivial involutions in Moreover we obtain a representation of (he SL(2, Am) ni terins of the ' so cahled Bruhat generator ami a complete set of relatioiis aniong them. Tlie order of the group SL(2, A,) is also calciilated. Finaily we coiistruct a remarkahle linear complex representation of t.he group SL(2. Am), for odd m, which generalizes the ciassical constructionof the Weil representation of the group SL(2, F), (lefined over a finite base fleid F of odd characteristic, associated to a non degenerate quadrat.ie space over P. A first decomposition of the Weil representation is indicated. |
|---|