Quantum Incompressibility and Razumov Stroganov Type Conjectures

We establish a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions. When the deformation parameter is a third root of unity, the representation degenerates and the wave functions coincide with the domain wall boundary condition partition function appearing in the conjecture of A.V. Razumov and Y.G. Stroganov. In particular, this gives a proof of the identification of the sum of the entries of the O(n) transfer matrix and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin.