Integrable System associated with genus 2 Macdonald polynomials

We present an interesting quantum integrable system with 3 degrees of freedom. Eigenfunctions of this system are new special functions — genus 2 Macdonald polynomials. This name is justified because these polynomials admit an action of genus 2 mapping class group, generalizing the $SL(2,\mathbb{Z})$ action for ordinary Macdonald polynomials. Using this integrable system, we conjecture certain new knot invariants.