Alternating sign matrices from a physicist point of view

There has recently been a convergence of interests between combinatorics and physics through the observation due to Razumov and Stroganov that the components of the ground state wave function of the 6-vertex (at a special value of the anisotropy parameter) model enumerate alternating sign matrices. This correspondence is still mysterious. I shall present one approach to the problem which uses the Macdonald polynomials and points towards a connection with the Quantum Hall Effect.