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Classification of the irreducible representations of semisimple Lie groups.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Vogan, David A. |
| Copyright Year | 1977 |
| Abstract | We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G, in terms of their restriction to a maximal compact subgroup K of G. (A classification in terms of analytic properties of the representations has been given by R. P. Langlands [(1973), mimeographed notes, Institute for Advanced Study, Princeton, NJ] for linear groups.) We first define a norm on the representations of K: if mu in K, mu is a nonnegative real number. Then if pi in G, mu is called a lowest K-type of pi if mu is minimal among the K-types occurring in pi. We announce a parameterization of the set of representations containing mu as a lowest K-type by the orbits of a finite group acting in a complex vector space (the dual of the vector part of a certain Cartan subgroup of G), and the result that mu necessarily occurs with multiplicity one in such representations. |
| File Format | PDF HTM / HTML |
| DOI | 10.1073/pnas.74.7.2649 |
| PubMed reference number | 16592410 |
| Journal | Medline |
| Volume Number | 74 |
| Issue Number | 7 |
| Alternate Webpage(s) | http://www.pnas.org/content/74/7/2649.full.pdf |
| Alternate Webpage(s) | https://doi.org/10.1073/pnas.74.7.2649 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
