Eisenstein integrals for theta stable parabolic subalgebras
| dc.creator | Binyong, Sun | |
| dc.date | 2004-03-25 | |
| dc.date | 2004-11-28 | |
| dc.date.accessioned | 2026-07-07T12:49:33Z | |
| dc.date.available | 2026-07-07T12:49:33Z | |
| dc.description | Let $G$ be a connected semisimple Lie group with a finite center, with a maximal compact subgroup $K$. There are two general methods to construct representations of $G$, namely, ordinary parabolic induction and cohomological parabolic induction. We define Eisenstein integrals relative to cohomological inductions which generalize Flensted-Jensen's fundamental functions for discrete series. They are analogous to Harish-Chandra's Eisenstein integrals related to ordinary inductions. We introduce the notion of Li positivity of a $K$ type in a representation of $G$ which is extremely useful in the study of branching laws. As an application of our integral, we show that the minimal $K$ types of many interesting representations are Li positive. These include all irreducible unitary representations with nonzero cohomology. | |
| dc.description | 53 pages, submitted to Invent. Math | |
| dc.identifier | https://arxiv.org/abs/math/0403440 | |
| dc.identifier | http://arxiv.org/abs/math/0403440 | |
| dc.identifier | Compositio Math. 143 (2007) 201-221 | |
| dc.identifier | doi:10.1112/S0010437X06002508 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222444 | |
| dc.subject | Representation Theory | |
| dc.subject | 22E30; 22E46 | |
| dc.title | Eisenstein integrals for theta stable parabolic subalgebras | |
| dc.type | text |