论文标题
准不变的Hermite多项式和Lassalle-Nekrasov对应
Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence
论文作者
论文摘要
Lassalle和Nekrasov在1990年代发现了具有谐音术语的理性Calogero-Moser系统与三角法版本之间的惊人对应关系。我们使用理性的Cherednik代数对这种对应关系进行了概念上的解释，并建立了其准不变扩展。 更具体地说，我们认为配置$ \ Mathcal A $具有多重性的真实超级平面，并承认有理的Baker-Akhiezer功能，并使用它来引入一类新的非对称多项式，我们将其称为$ \ MATHCAL为$ -HEMCAL是$ -HEMERCAL。这些多项式在$ \ Mathcal a $ quasi-invariants的空间中形成线性基础，这是具有谐波术语的相应广义有理calogero-moser运算符的特征。在类型$ a_n $的Coxeter配置的情况下，这会导致Lassalle-Nekrasov通信及其高阶类似物的准不变版本。
Lassalle and Nekrasov discovered in the 1990s a surprising correspondence between the rational Calogero-Moser system with a harmonic term and its trigonometric version. We present a conceptual explanation of this correspondence using the rational Cherednik algebra and establish its quasi-invariant extension. More specifically, we consider configurations $\mathcal A$ of real hyperplanes with multiplicities admitting the rational Baker-Akhiezer function and use this to introduce a new class of non-symmetric polynomials, which we call $\mathcal A$-Hermite polynomials. These polynomials form a linear basis in the space of $\mathcal A$-quasi-invariants, which is an eigenbasis for the corresponding generalised rational Calogero-Moser operator with harmonic term. In the case of the Coxeter configuration of type $A_N$ this leads to a quasi-invariant version of the Lassalle-Nekrasov correspondence and its higher order analogues.
