AI 中文总结
该研究通过证明广义Jack多项式Selberg平均的全阶因子化公式，结合广义Cauchy恒等式，完成一般β下带四个基本超多重态的四点SU(2)AGT对应关系的全阶证明，将双分划项与Nekrasov不动点贡献对应。
AI 中文摘要
我们通过证明广义Jack多项式的Selberg平均的全阶因子化公式，给出了一般β=-ε₁/ε₂下带四个基本超多重态的四点SU(2)AGT对应关系的全阶证明。对广义Macdonald Pieri规则取系数-wise Jack极限，我们在严格Cauchy对偶基中得到所需的单盒矩阵元。有理角函数恒等式随后对所有父双分划求和，而Selberg核的显式全导数在Dotsenko-Fateev电荷平衡超平面上产生三角递推。该递推的唯一解是此前仅通过有限阶验证的广义Kadell公式。结合该结果与广义Cauchy恒等式，可将每个双分划项与对应的Nekrasov不动点贡献对应起来。
英文摘要
We give an all-level proof of the four-point $SU(2)$ AGT correspondence with four fundamental hypermultiplets at generic $β=-ε_1/ε_2$, by proving an all-level factorization formula for Selberg averages of generalized Jack polynomials. Taking a coefficientwise Jack limit of the generalized Macdonald Pieri rule, we obtain the required one-box matrix elements in the strict Cauchy dual basis. A rational corner-function identity then evaluates the sum over all parent double partitions, while an explicit total derivative of the Selberg kernel yields a triangular recursion on the Dotsenko-Fateev charge balance hyperplane. The unique solution of this recursion is the generalized Kadell formula previously verified only through finite level. Combining this result with the generalized Cauchy identity identifies each double partition term with the corresponding Nekrasov fixed-point contribution.
Comments7+14 pages
