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Square Integrable Representations of Semisimple Lie Groups
| Content Provider | Scilit |
|---|---|
| Author | Tirao, Juan A. |
| Copyright Year | 1974 |
| Description | Let D be a bounded symmetric domain. Let G be the universal covering group of the identity component of the group of all holomorphic diffeomorphisms of D onto itself. In this case, any G-homogeneous vector bundle admits a natural structure of G-homogeneous holomorphic vector bundles. The vector bundle must be holomorphically trivial, since D is a Stein manifold. We exhibit explicitly a holomorphic trivialization of by defining a map (V being the fiber of the vector bundle) which extends the classical ``universal factor of automorphy'' for the action of on D. Then, we study the space H of all square integrable holomorphic sections of . The natural action of G on H defines a unitary irreducible representation of G. The representations obtained in this way are square integrable over (Z denotes the center of G) in the sense that the absolute values of their matrix coefficients are in . |
| Related Links | http://www.ams.org/tran/1974-190-00/S0002-9947-1974-0338270-X/S0002-9947-1974-0338270-X.pdf |
| Ending Page | 75 |
| Page Count | 19 |
| Starting Page | 57 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1996950 |
| Journal | Transactions of the American Mathematical Society |
| Volume Number | 190 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Semisimple Lie Lie Groups Square Integrable Representations |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
