Operator K-Theory and Tempiric Representations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929648552640512 |
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| author | Bradd, Jacob Higson, Nigel Yuncken, Robert |
| author_facet | Bradd, Jacob Higson, Nigel Yuncken, Robert |
| contents | David Vogan proved that if $G$ is a real reductive group, and if $K$ is a maximal compact subgroup of $G$, then every irreducible representation of $K$ is included as a minimal $K$-type in precisely one tempered, irreducible unitary representation of $G$ with real infinitesimal character, and that moreover it is included there with multiplicity one and is the unique minimal $K$-type in that representation. We shall prove that the Connes-Kasparov isomorphism in operator $K$-theory is equivalent to a $K$-theoretic version of Vogan's result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18924 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator K-Theory and Tempiric Representations Bradd, Jacob Higson, Nigel Yuncken, Robert Representation Theory K-Theory and Homology Operator Algebras 22E45, 22E46, 46L80 David Vogan proved that if $G$ is a real reductive group, and if $K$ is a maximal compact subgroup of $G$, then every irreducible representation of $K$ is included as a minimal $K$-type in precisely one tempered, irreducible unitary representation of $G$ with real infinitesimal character, and that moreover it is included there with multiplicity one and is the unique minimal $K$-type in that representation. We shall prove that the Connes-Kasparov isomorphism in operator $K$-theory is equivalent to a $K$-theoretic version of Vogan's result. |
| title | Operator K-Theory and Tempiric Representations |
| topic | Representation Theory K-Theory and Homology Operator Algebras 22E45, 22E46, 46L80 |
| url | https://arxiv.org/abs/2412.18924 |