Linear recurrence relations in $Q$-systems and difference $L$-operators

TL;DR

This paper explores linear recurrence relations in the character solutions of $Q$-systems derived from Kirillov-Reshetikhin modules, using difference $L$-operators to construct and conjecture properties of these recurrences.

Contribution

It provides a uniform construction of linear recurrences in $Q$-systems based on difference $L$-operators and formulates conjectural properties of these recurrences.

Findings

Known results on difference $L$-operators inform the construction of linear recurrences.

A uniform method for constructing recurrences in various examples is proposed.

Conjectural properties of the recurrences are formulated.

Abstract

We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in many examples, and formulate certain conjectural properties predicted in general by this construcion.