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arXiv · 2603.23120

Quasi-particles and the Kanade-Russell and Kur\c{s}ung\"{o}z formula for Capparelli's identity

Marijana Butorac·Slaven Kožić·Mirko Primc
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Abstract

We construct a quasi-particle basis of the integrable highest weight module of highest weight $3\Lambda_0$ 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 Kur\c{s}ung\"{o}z's Andrews-Gordon type series of Capparelli's identities.

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Marijana Butorac, Slaven Kožić, Mirko Primc. 2026-03-24. Quasi-particles and the Kanade-Russell and Kur\c{s}ung\"{o}z formula for Capparelli's identity. https://arxiv.org/abs/2603.23120

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