Modified Macdonald polynomials and integrability

Abstract

We derive combinatorial formulae for the modified Macdonald polynomial $H_{\lambda }(x;q,t)$ using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivation is based on an integrable model associated to the quantum group of $U_{q}(\wide{sl}_{n+1})$.

References corrected, explanations and examples added