We provide first a purely VOA-theoretic guide to the theory of coordinate transformations for a VOA in direct accordance with its first appearance in a paper of Zhu. Among these results, we are able to obtain new closed-form expressions for the square-bracket Heisenberg modes. We then elaborate on the connection to p-adic modular forms which arise as characters of states in p-adic VOAs. In particular, we show that the image of the p-adic character map for the p-adic Heisenberg VOA contains infinitely-many p-adic modular forms of level one which are not quasi-modular. Finally, we introduce a new VOA structure obtained from the Artin-Hasse exponential, and serving as the p-adic analogue of the square-bracket formalism. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/28468 |
| Date | January 2023 |
| Creators | Barake, Daniel |
| Contributors | Franc, Cameron, Mathematics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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