Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Hecke-type double-sums and general string functions for the affine Lie algebra $A_{1}^{(1)}$

Eric T. Mortenson

Abstract

We demonstrate how formulas that express Hecke-type double-sums in terms of theta functions and Appell--Lerch functions -- the building blocks of Ramanujan's mock theta functions -- can be used to give general string function formulas for the affine Lie algebra $A_{1}^{(1)}$ for levels $N=1,2,3,4$.

On Hecke-type double-sums and general string functions for the affine Lie algebra $A_{1}^{(1)}$

Abstract

We demonstrate how formulas that express Hecke-type double-sums in terms of theta functions and Appell--Lerch functions -- the building blocks of Ramanujan's mock theta functions -- can be used to give general string function formulas for the affine Lie algebra for levels .

Paper Structure

This paper contains 19 sections, 29 theorems, 142 equations.

Table of Contents

  1. Notation
  2. Introduction
  3. Preliminaries
  4. Theta functions
  5. Appell--Lerch functions
  6. Hecke-type double-sums
  7. The general integral-level string function
  8. Computing the general level $N=1$ string function
  9. Computing the general level $N=2$ string function
  10. Computing the general level $N=3$ string function
  11. Computing the general level $N=4$ string function
  12. Computing level $N=2$ string functions: Examples
  13. The string function $c_{20}^{20}-c_{02}^{20}$ (\ref{['equation:KP-2-List2-A']}):
  14. Computing level $N=3$ string functions: Examples
  15. The string function $c_{12}^{30}$ (\ref{['equation:KP-3-List2-A']}):
  16. ...and 4 more sections

Key Result

Theorem 2.1

MPS We have

Theorems & Definitions (40)

  • Theorem 2.1
  • Corollary 2.2
  • Corollary 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Theorem 2.7
  • Proposition 3.1
  • Proposition 3.2
  • Lemma 3.3
  • ...and 30 more