False theta functions and the Verlinde formula - Creutzig, Thomas; Milas, Antun (Advances in Mathematics, 2014)
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. © 2014 Elsevier Inc.
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Keywords: False and partial theta functions; Logarithmic conformal field theories; Modular forms; Verlinde formula; Vertex operator algebras