On Whittaker modules over a class of algebras similar to $U(sl_{2})$
| dc.creator | Tang, Xin | |
| dc.date | 2006-10-29 | |
| dc.date.accessioned | 2026-07-07T07:29:35Z | |
| dc.date.available | 2026-07-07T07:29:35Z | |
| dc.description | Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by Smith in \cite{S}. Since the introduction of these algebras, research efforts have been focused on understanding their weight modules, and many important results were already obtained in \cite{S} and \cite{Ku}. But it seems that not much has been done on the part of nonweight modules. In this note, we generalize Kostant's results in \cite{K} on the Whittaker model for the universal enveloping algebras $U(\frak g)$ of finite dimensional semisimple Lie algebras $\frak g$ to Smith's algebras. As a result, a complete classification of irreducible Whittaker modules (which are definitely infinite dimensional) for Smith's algebras is obtained, and the submodule structure of any Whittaker module is also explicitly described. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610897 | |
| dc.identifier | http://arxiv.org/abs/math/0610897 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118166 | |
| dc.subject | Representation Theory | |
| dc.subject | Primary 17B55, 20G; Secondary 17B50 | |
| dc.title | On Whittaker modules over a class of algebras similar to $U(sl_{2})$ | |
| dc.type | text |