W-algebras, higher rank false theta functions, and quantum dimensions

Kathrin Bringmann; Antun Milas

doi:10.1007/s00029-016-0289-z

W-algebras, higher rank false theta functions, and quantum dimensions

Kathrin Bringmann
, Antun Milas

Mathematics and Statistics

University at Albany

University of Cologne

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Motivated by appearances of Rogers’ false theta functions in the representation theory of the singlet vertex operator algebra, for each finite-dimensional simple Lie algebra of ADE type, we introduce higher rank false theta functions as characters of atypical modules of certain W-algebras and compute asymptotics of irreducible characters which allows us to determine quantum dimensions of the corresponding modules. In the s ℓ₂-case, we recover many results from Bringmann and Milas (IMRN 21:11351–11387, 2015).

Original language	English
Pages (from-to)	1249-1278
Number of pages	30
Journal	Selecta Mathematica, New Series
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s00029-016-0289-z
State	Published - Apr 1 2017

Keywords

Characters
False theta functions
Jacobi forms
Modular forms
Vertex algebras

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AB - Motivated by appearances of Rogers’ false theta functions in the representation theory of the singlet vertex operator algebra, for each finite-dimensional simple Lie algebra of ADE type, we introduce higher rank false theta functions as characters of atypical modules of certain W-algebras and compute asymptotics of irreducible characters which allows us to determine quantum dimensions of the corresponding modules. In the s ℓ2-case, we recover many results from Bringmann and Milas (IMRN 21:11351–11387, 2015).

KW - Characters

KW - False theta functions

KW - Jacobi forms

KW - Modular forms

KW - Vertex algebras

UR - https://www.scopus.com/pages/publications/84991781040

U2 - 10.1007/s00029-016-0289-z

DO - 10.1007/s00029-016-0289-z

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JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 2

ER -

W-algebras, higher rank false theta functions, and quantum dimensions

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Keywords

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