Quantum incompressibility and Razumov Stroganov type conjectures

TL;DR

This paper links polynomial representations of algebraic structures to quantum Hall wave functions, proving a conjecture relating transfer matrix eigenvectors and six-vertex model partition functions at roots of unity.

Contribution

It establishes a novel correspondence between algebraic representations and quantum Hall wave functions, providing a new proof of a Razumov-Stroganov conjecture.

Findings

Proved the Razumov-Stroganov type conjecture at roots of unity.

Connected algebraic degenerations to specific quantum Hall wave functions.

Provided an alternative proof for the relation between transfer matrix eigenvectors and six-vertex model partition functions.

Abstract

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 a O(n) transfer matrix eigenvector and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin.