# Macdonald operators and quantum Q-systems for classical types

## TL;DR

This paper introduces solutions to quantum Q-systems of types B, C, D using q-difference operators, extending previous work on type A, and conjectures their role in acting on q-Whittaker functions related to KR-modules.

## Contribution

It generalizes the construction of quantum Q-systems to classical types using q-difference operators and links these to Macdonald-van Diejen operators and q-Whittaker functions.

## Key findings

- Constructed solutions for types B, C, D quantum Q-systems.
- Connected q-difference operators to Macdonald-van Diejen operators.
- Conjectured operators act as raising/lowering operators for q-Whittaker functions.

## Abstract

We propose solutions of the quantum Q-systems of types $B_N,C_N,D_N$ in terms of $q$-difference operators, generalizing our previous construction for the Q-system of type $A$. The difference operators are interpreted as $q$-Whittaker limits of discrete time evolutions of Macdonald-van Diejen type operators. We conjecture that these new operators act as raising and lowering operators for $q$-Whittaker functions, which are special cases of graded characters of fusion products of KR-modules.