On translation invariant symmetric polynomials and Haldane's conjecture

Details On translation invariant symmetric polynomials and Haldane's conjecture On translation invariant symmetric polynomials and Haldane's conjecture

2010-04-02

arxiv.org/abs/1004.0364v1

Topology and Physics: Proceedings of the Nankai International Conference in Memory of Xiao-Song Lin, Nankai Tracts in Mathemat

Mathematics

Combinatorics

7 pages, 1 figure. Presentation improved over the published version.

Scientific paper

We show that the ring of translation invariant symmetric polynomials in n variables is isomorphic to the full polynomial ring in n-1 variables, in characteristic 0. We disprove a conjecture of Haldane regarding the structure of such polynomials. Our motivation is the fractional quantum Hall effect, where translation invariant (anti)symmetric complex n-variate polynomials characterize n-electron wavefunctions.

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