Higher rank partial and false theta functions and representation theory

Creutzig T, Milas A (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Advances in Mathematics Elsevier

Book Volume: 314

Pages Range: 203-227

DOI: 10.1016/j.aim.2017.04.027

Abstract

We study higher rank Jacobi partial and false theta functions (generalizations of the classical partial and false theta functions) associated to positive definite rational lattices. In particular, we focus our attention on certain Kostant's partial theta functions coming from ADE root lattices, which are then linked to representation theory of W-algebras. We derive modular transformation properties of regularized higher rank partial and false theta functions as well as Kostant's version of these. Modulo conjectures in representation theory, as an application, we compute regularized quantum dimensions of atypical and typical modules of “narrow” logarithmic W-algebras associated to rescaled root lattices. This paper substantially generalize our previous work [19] pertaining to (1,p)-singlet W-algebras (the sl2 case). Results in this paper are very general and are applicable in a variety of situations.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

University of Alberta CA Canada (CA) Max-Planck-Institut für Mathematik (MPIM) DE Germany (DE)

How to cite

APA:

Creutzig, T., & Milas, A. (2017). Higher rank partial and false theta functions and representation theory. Advances in Mathematics, 314, 203-227. https://doi.org/10.1016/j.aim.2017.04.027

MLA:

Creutzig, Thomas, and Antun Milas. "Higher rank partial and false theta functions and representation theory." Advances in Mathematics 314 (2017): 203-227.

BibTeX: Download