Whittaker Modules for Generalized Weyl Algebras
| dc.creator | Benkart, Georgia | |
| dc.creator | Ondrus, Matthew | |
| dc.date | 2008-03-25 | |
| dc.date.accessioned | 2026-07-07T09:28:18Z | |
| dc.date.available | 2026-07-07T09:28:18Z | |
| dc.description | We investigate Whittaker modules for generalized Weyl algebras, a class of associative algebras which includes the quantum plane, Weyl algebras, the universal enveloping algebra of sl_2 and of Heisenberg Lie algebras, Smith's generalizations of U(sl_2), various quantum analogues of these algebras, and many others. We show that the Whittaker modules V = Aw of the generalized Weyl algebra A = R(phi,t) are in bijection with the phi-stable left ideals of R. We determine the annihilator Ann_A(w) of the cyclic generator w of V. We also describe the annihilator ideal Ann_A(V) under certain assumptions that hold for most of the examples mentioned above. As one special case, we recover Kostant's well-known results on Whittaker modules and their associated annihilators for U(sl_2). | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/0803.3570 | |
| dc.identifier | http://arxiv.org/abs/0803.3570 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157408 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 (Primary); 16D60 (Secondary) | |
| dc.title | Whittaker Modules for Generalized Weyl Algebras | |
| dc.type | text |