Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917350507282432 |
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| author | Haller, Stefan |
| author_facet | Haller, Stefan |
| contents | We study the Rumin differentials of the 5-dimensional graded nilpotent Lie group that appears as osculating group of generic rank two distributions in dimension five. In irreducible unitary representations of this group, the Rumin differentials provide intriguing generalizations of the classical quantum harmonic oscillator. For the Schrodinger representations, we compute the spectrum and the zeta regularized determinant of each Rumin differential. In the generic representations, we evaluate their alternating product, i.e., the analytic torsion of the Rumin complex. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_11159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group Haller, Stefan Spectral Theory Mathematical Physics Differential Geometry Representation Theory 58J52 (primary) and 11M41, 34L40, 53C17, 58A30, 58J10, 81Q20, 81Q80 We study the Rumin differentials of the 5-dimensional graded nilpotent Lie group that appears as osculating group of generic rank two distributions in dimension five. In irreducible unitary representations of this group, the Rumin differentials provide intriguing generalizations of the classical quantum harmonic oscillator. For the Schrodinger representations, we compute the spectrum and the zeta regularized determinant of each Rumin differential. In the generic representations, we evaluate their alternating product, i.e., the analytic torsion of the Rumin complex. |
| title | Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group |
| topic | Spectral Theory Mathematical Physics Differential Geometry Representation Theory 58J52 (primary) and 11M41, 34L40, 53C17, 58A30, 58J10, 81Q20, 81Q80 |
| url | https://arxiv.org/abs/2309.11159 |