关于平移不变的对称多项式和Haldinger猜想
On translation invariant symmetric polynomials and Haldane's conjecture
摘要：
证明了n元平移不变对称多项式环同构于n-1元全多项式环，其特征为0。我们反驳的猜想Halflit关于结构的多项式。我们的动机是分数量子霍尔效应，其中平移不变（反对）对称复n变量多项式表征n电子波函数。
英文摘要：
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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