The Fock-Schwartz spin representation space
In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the infinitesim...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/140007 |
| _version_ | 1811088730313719808 |
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| author | Valiveti, Kaavya G. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Valiveti, Kaavya G. |
| author_sort | Valiveti, Kaavya G. |
| collection | MIT |
| description | In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the infinitesimal actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold. |
| first_indexed | 2024-09-23T14:06:38Z |
| format | Thesis |
| id | mit-1721.1/140007 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T14:06:38Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1400072022-02-08T03:25:35Z The Fock-Schwartz spin representation space Valiveti, Kaavya G. Massachusetts Institute of Technology. Department of Mathematics In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the infinitesimal actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold. Ph.D. 2022-02-07T15:18:35Z 2022-02-07T15:18:35Z 2021-09 2021-08-31T18:22:38.455Z Thesis https://hdl.handle.net/1721.1/140007 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Valiveti, Kaavya G. The Fock-Schwartz spin representation space |
| title | The Fock-Schwartz spin representation space |
| title_full | The Fock-Schwartz spin representation space |
| title_fullStr | The Fock-Schwartz spin representation space |
| title_full_unstemmed | The Fock-Schwartz spin representation space |
| title_short | The Fock-Schwartz spin representation space |
| title_sort | fock schwartz spin representation space |
| url | https://hdl.handle.net/1721.1/140007 |
| work_keys_str_mv | AT valivetikaavyag thefockschwartzspinrepresentationspace AT valivetikaavyag fockschwartzspinrepresentationspace |