The Orbit Method and Character Formulas for Tempered representations of a Nonconnected Reductive Real Algebraic Group
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917227188453376 |
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| author | Ducloux, Jean-Yves |
| author_facet | Ducloux, Jean-Yves |
| contents | Let G be a possibly disconnected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. I then describe these characters using certain ``Kirillov's formulas,'' based on the descent method near each elliptic element in G. If G is linear and connected, the parameters I use are ``final basic'' parameters in the sense of Knapp and Zuckerman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20384 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Orbit Method and Character Formulas for Tempered representations of a Nonconnected Reductive Real Algebraic Group Ducloux, Jean-Yves Representation Theory Let G be a possibly disconnected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. I then describe these characters using certain ``Kirillov's formulas,'' based on the descent method near each elliptic element in G. If G is linear and connected, the parameters I use are ``final basic'' parameters in the sense of Knapp and Zuckerman. |
| title | The Orbit Method and Character Formulas for Tempered representations of a Nonconnected Reductive Real Algebraic Group |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.20384 |