论文标题
AFLT型Selberg积分
AFLT-type Selberg integrals
论文作者
论文摘要
在2011年关于AGT猜想的论文中，Alba，Fateev，Litvinov和Tarnopolsky（AFLT）对Selberg积分的封闭式评估是对两个Jack多项式产品的积分，从而统一了众所周知的Kadell和Hua和Hua和Hua和Kadell Integrals。在本文中，我们使用各种对称函数和对称功能技术来证明AFLT积分的概括。其中包括（i）AFLT积分的$ \ Mathrm {a} _n $类似物，其中包含intapterand中的两个插孔多项式； （ii）（i）以$γ= 1 $（schur或gue案例）的概括，其中包含$ n+1 $ schur函数的产品； （iii）AFLT积分的椭圆概括，其中千斤顶多项式的作用由一对椭圆插值函数播放； （iv）麦克唐纳多项式的AFLT积分。
In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for a Selberg integral over the product of two Jack polynomials, thereby unifying the well-known Kadell and Hua--Kadell integrals. In this paper we use a variety of symmetric functions and symmetric function techniques to prove generalisations of the AFLT integral. These include (i) an $\mathrm{A}_n$ analogue of the AFLT integral, containing two Jack polynomials in the integrand; (ii) a generalisation of (i) for $γ=1$ (the Schur or GUE case), containing a product of $n+1$ Schur functions; (iii) an elliptic generalisation of the AFLT integral in which the role of the Jack polynomials is played by a pair of elliptic interpolation functions; (iv) an AFLT integral for Macdonald polynomials.
