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On the Irreducibility of Nonunitary Induced Representations of Certain Semidirect Products
| Content Provider | Scilit |
|---|---|
| Author | Thieleker, Ernest |
| Copyright Year | 1972 |
| Description | Let G be a connected Lie group which is a semidirect product of a compact subgroup K and a normal solvable subgroup S. Let be a character of S, and let be the stabilizer of in K. Let be a finite-dimensional irreducible representation of the subgroup on the complex vector space H. In this paper we consider the induced representations of G on various Banach spaces, and study their topological irreducibility. The basic method used consists in studying the irreducibility of the Lie algebra representations which arise on the linear subspaces of K-finite vectors. The latter question then can be reduced to the problem of determining when certain modules over certain commutative algebras are irreducible. The method discussed in this paper leads to two theorems giving sufficient conditions on the character that the induced representations be topologically irreducible. The question of infinitesimal equivalence of various induced representations is also discussed. |
| Related Links | http://www.ams.org/tran/1972-164-00/S0002-9947-1972-0293017-9/S0002-9947-1972-0293017-9.pdf |
| Ending Page | 369 |
| Page Count | 17 |
| Starting Page | 353 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1995981 |
| Journal | Transactions of the American Mathematical Society |
| Volume Number | 164 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Logic Mathematical Physics Induced Representations Nonunitary Induced Semidirect Products Irreducibility of Nonunitary |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
