论文标题
超级杰克多项式和相关的套件的新正交关系 - nekrasov通信
New orthogonality relations for super-Jack polynomials and an associated Lassalle--Nekrasov correspondence
论文作者
论文摘要
由Kerov，Okounkov和Olshanski引入的超级杰克多项式是$ n+m $变量中的多项式，当$ n = 0 $ n = 0 $或$ m = 0 $时，它们会减少插孔多项式，并提供Trigormetric deformetrord deformEdementrormeDementrormeDementrormeDementrormeDormed calogered calogered calogeredcalogerederland calogered-moserserland的量子eigenfunctions。我们证明，超级杰克多项式相对于$（p，q）\ mapsto（l_pq）（0）$的双线性形式的双线性形式是正交的，具有$ l_p $ l_p $量子积分。此外，我们还提供了三角和谐波变形的Calogero-Moser-sutherland系统与超级高铁多项式的正交性（提供后一种系统的关节特征功能）之间的新的谐波和谐波变形的Calogero-Moser-Sutherland系统和推断正交性之间的新证明。
The super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are polynomials in $n+m$ variables, which reduce to the Jack polynomials when $n=0$ or $m=0$ and provide joint eigenfunctions of the quantum integrals of the trigonometric deformed Calogero-Moser-Sutherland system. We prove that the super-Jack polynomials are orthogonal with respect to a bilinear form of the form $(p,q)\mapsto (L_pq)(0)$, with $L_p$ quantum integrals of the rational deformed Calogero-Moser-Sutherland system. In addition, we provide a new proof of the Lassalle-Nekrasov correspondence between trigonometric and rational harmonic deformed Calogero-Moser-Sutherland systems and infer orthogonality of super-Hermite polynomials, which provide joint eigenfunctions of the latter system.
