Generalized Harish-Chandra Modules: A New Direction
| dc.creator | Penkov, Ivan | |
| dc.creator | Zuckerman, Gregg | |
| dc.date | 2003-10-09 | |
| dc.date.accessioned | 2026-07-07T05:01:46Z | |
| dc.date.available | 2026-07-07T05:01:46Z | |
| dc.description | Let $\frak g$ be a reductive Lie algebra over $\bold C$. We say that a $\frak g$-module $M$ is a generalized Harish-Chandra module if, for some subalgebra $\frak k \subset\frak g$, $M$ is locally $\frak k$-finite and has finite $\frak k$-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when $\frak k$ is a Cartan subalgebra. We also review the recent determination of which reductive in $\frak g$ subalgebras $\frak k$ are essential to a classification. Finally, we present in detail the emerging picture for the case when $\frak k$ is a principal 3-dimensional subalgebra. | |
| dc.identifier | https://arxiv.org/abs/math/0310140 | |
| dc.identifier | http://arxiv.org/abs/math/0310140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68802 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B10 | |
| dc.title | Generalized Harish-Chandra Modules: A New Direction | |
| dc.type | text |