A generating function for Blattner's formula
| dc.creator | Willenbring, Jeb F. | |
| dc.creator | Zuckerman, Gregg J. | |
| dc.date | 2006-12-11 | |
| dc.date | 2006-12-17 | |
| dc.date.accessioned | 2026-07-07T07:35:31Z | |
| dc.date.available | 2026-07-07T07:35:31Z | |
| dc.description | Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner's formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and is valid for any discrete series system. Other results include a new proof of a symmetry of Blattner's formula, and a positivity result for certain low rank examples. We consider in detail the situation for G of type split G_2. The motivation for this work came from an attempt to understand pictures coming from Blattner's formula, some of which we include in the paper. | |
| dc.description | 12 pages, 4 figures, added section on a positivity result | |
| dc.identifier | https://arxiv.org/abs/math/0612266 | |
| dc.identifier | http://arxiv.org/abs/math/0612266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120120 | |
| dc.subject | Representation Theory | |
| dc.title | A generating function for Blattner's formula | |
| dc.type | text |