Inverse spectral results for non-abelian group actions
© 2020 Royal Dutch Mathematical Society (KWG) In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a compact Lie group acting isometrically on a compac...
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| Format: | Article |
| Language: | English |
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Elsevier BV
2021
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| Online Access: | https://hdl.handle.net/1721.1/134048 |
| _version_ | 1826188166013386752 |
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| author | Guillemin, Victor Wang, Zuoqin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guillemin, Victor Wang, Zuoqin |
| author_sort | Guillemin, Victor |
| collection | MIT |
| description | © 2020 Royal Dutch Mathematical Society (KWG) In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a compact Lie group acting isometrically on a compact Riemannian manifold X. We will show that for the Schrödinger operator −ħ2Δ+V with V∈C∞(X)G, the potential function V is, in some interesting examples, determined by the G-equivariant spectrum. The key ingredient in this proof is a generalized Legendrian relation between the Lagrangian manifolds Graph(dV) and Graph(dF), where F is a spectral invariant defined on an open subset of the positive Weyl chamber. |
| first_indexed | 2024-09-23T07:55:33Z |
| format | Article |
| id | mit-1721.1/134048 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T07:55:33Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1340482023-02-16T20:40:21Z Inverse spectral results for non-abelian group actions Guillemin, Victor Wang, Zuoqin Massachusetts Institute of Technology. Department of Mathematics © 2020 Royal Dutch Mathematical Society (KWG) In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a compact Lie group acting isometrically on a compact Riemannian manifold X. We will show that for the Schrödinger operator −ħ2Δ+V with V∈C∞(X)G, the potential function V is, in some interesting examples, determined by the G-equivariant spectrum. The key ingredient in this proof is a generalized Legendrian relation between the Lagrangian manifolds Graph(dV) and Graph(dF), where F is a spectral invariant defined on an open subset of the positive Weyl chamber. 2021-10-27T19:57:47Z 2021-10-27T19:57:47Z 2021 2021-05-20T13:44:45Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134048 en 10.1016/J.INDAG.2020.05.004 Indagationes Mathematicae Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Guillemin, Victor Wang, Zuoqin Inverse spectral results for non-abelian group actions |
| title | Inverse spectral results for non-abelian group actions |
| title_full | Inverse spectral results for non-abelian group actions |
| title_fullStr | Inverse spectral results for non-abelian group actions |
| title_full_unstemmed | Inverse spectral results for non-abelian group actions |
| title_short | Inverse spectral results for non-abelian group actions |
| title_sort | inverse spectral results for non abelian group actions |
| url | https://hdl.handle.net/1721.1/134048 |
| work_keys_str_mv | AT guilleminvictor inversespectralresultsfornonabeliangroupactions AT wangzuoqin inversespectralresultsfornonabeliangroupactions |