Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quasi-particles and the Kanade-Russell and Kurşungöz formula for Capparelli's identity

Marijana Butorac, Slaven Kožić, Mirko Primc

Abstract

We construct a quasi-particle basis of the integrable highest weight module of highest weight $3Λ_0$ for the twisted affine Lie algebra of type $A_2^{(2)}$ in the principal realization. More specifically, by introducing the concept of polychromatic quasi-particle and finding relations among quasi-particles, we construct the spanning set of the standard module. Finally, its linear independence is proved by using Kanade-Russell and Kurşungöz's Andrews-Gordon type series of Capparelli's identities.

Quasi-particles and the Kanade-Russell and Kurşungöz formula for Capparelli's identity

Abstract

We construct a quasi-particle basis of the integrable highest weight module of highest weight for the twisted affine Lie algebra of type in the principal realization. More specifically, by introducing the concept of polychromatic quasi-particle and finding relations among quasi-particles, we construct the spanning set of the standard module. Finally, its linear independence is proved by using Kanade-Russell and Kurşungöz's Andrews-Gordon type series of Capparelli's identities.
Paper Structure (8 sections, 8 theorems, 108 equations)

This paper contains 8 sections, 8 theorems, 108 equations.

Table of Contents

  1. Preliminaries on vertex operator construction
  2. Quasi-particles for the Lie algebra $A_2^{(2)}$
  3. Quasi-particle basis of the $A_2^{(2)}$-module $L(3\Lambda_0)$
  4. Relations for quasi-particles
  5. Proof of Theorem \ref{['main_thm']}
  6. Initial conditions
  7. Spanning set
  8. Linear independence

Key Result

Lemma 2.1

For fixed $\alpha, \delta \in \Phi$ and $\beta=\nu (\alpha)$, we have

Theorems & Definitions (18)

  • Example 1
  • Lemma 2.1
  • Definition 3.1
  • Theorem 3.1
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • proof
  • ...and 8 more