Reflecting (on) the modulo 9 Kanade--Russell (conjectural) identities

TL;DR

This paper investigates the complexity and versatility of five modulo 9 Kanade--Russell identities by analyzing their finite polynomial forms and their behavior under the $q o 1/q$ reflection, revealing new insights into their structure.

Contribution

The paper introduces a detailed analysis of the finite versions and reflection images of the modulo 9 Kanade--Russell identities, expanding understanding of their properties.

Findings

Finite polynomial versions exhibit specific structural patterns.

Reflection under $q o 1/q$ reveals symmetries and dualities.

Enhanced comprehension of the identities' complexity and versatility.

Abstract

We examine complexity and versatility of five modulo 9 Kanade--Russell identities through their finite (aka polynomial) versions and images under the $q\mapsto1/q$ reflection.