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On the characters of a certain series of N=4 superconformal modules II

Minoru Wakimoto

Abstract

In this paper we compute the characters of certain non-irreducible N=4 superconformal modules which are different from the ones treated in our previous paper, and study their relation with characters of N=2 superconformal modules. Also, for these non-irreducible N=4 modules, we deduce the expression of characters in terms of string functions.

On the characters of a certain series of N=4 superconformal modules II

Abstract

In this paper we compute the characters of certain non-irreducible N=4 superconformal modules which are different from the ones treated in our previous paper, and study their relation with characters of N=2 superconformal modules. Also, for these non-irreducible N=4 modules, we deduce the expression of characters in terms of string functions.
Paper Structure (17 sections, 37 theorems, 61 equations)

This paper contains 17 sections, 37 theorems, 61 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Characters of N=2 superconformal modules
  4. Integrable modules of $\widehat{sl}(2|1)$
  5. Characters of principal admissible $\widehat{sl}(2|1)$-modules
  6. Twisted $\widehat{sl}(2|1)$-characters
  7. Quantum Hamiltonian reduction of $\widehat{sl}(2|1)$-modules
  8. Characters of $\widehat{A}(1,1)$-modules
  9. Characters of integrable $\widehat{A}(1,1)$-modules
  10. Characters of principal admissible $\widehat{A}(1,1)$-modules
  11. Twisted $\widehat{A}(1,1)$-characters
  12. Characters of non-irreducible $\widehat{A}(1,1)$-modules
  13. Characters of N=4 superconformal modules
  14. Quantum Hamiltonian reduction of $\widehat{A}(1,1)$-module
  15. Non-irreducible N=4 modules
  16. ...and 2 more sections

Key Result

Lemma 2.1

Let $M \in {\mathbf N}$, $m \in \frac{1}{2} {\mathbf N}$, $s \in \frac{1}{2} {\mathbf Z}$ and $\varepsilon \in {\mathbf R}$ such that $(M,2m)=1$. Then the following formulas hold for $j, \, k \in {\mathbf R}$ such that $0<j,k<M$.

Theorems & Definitions (42)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • proof
  • proof
  • Lemma 3.1
  • Lemma 3.2
  • ...and 32 more