Article ID Journal Published Year Pages File Type
4665716 Advances in Mathematics 2014 26 Pages PDF
Abstract

We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of WW-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)W(2,2p−1), we formulate a Verlinde-type formula for the fusion rules of irreducible W(2,2p−1)W(2,2p−1)-modules.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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