Abstract
We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal field theory, first, we are able to determine modular-like transformation properties of regularized partial and false theta functions. Then, after suitable identification of regularized partial/false theta functions with the characters of atypical modules for the singlet vertex algebra W(2,2p-1), we formulate a Verlinde-type formula for the fusion rules of irreducible W(2,2p-1)-modules.
| Original language | English |
|---|---|
| Pages (from-to) | 520-545 |
| Number of pages | 26 |
| Journal | Advances in Mathematics |
| Volume | 262 |
| DOIs | |
| State | Published - Sep 10 2014 |
Keywords
- False and partial theta functions
- Logarithmic conformal field theories
- Modular forms
- Verlinde formula
- Vertex operator algebras
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