Quasi-particles and the Kanade-Russell and Kursung\"oz formula for Capparelli's identity
Abstract
We construct a quasi-particle basis of the integrable highest weight module of highest weight 30 for the twisted affine Lie algebra of type A2(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 Kursung\"oz's Andrews-Gordon type series of Capparelli's identities.
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