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 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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2021

Author dc:creator

• Valiveti, Kaavya G.

Advisor dc:contributor.advisor

• Melrose, Richard B.

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright MIT

Licence dc:rights.uri

• http://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/140007

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/140007