论文标题
在Selberg积分的Dotsenko-Fateev复合物及其扩展上
On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
论文作者
论文摘要
Selberg积分具有以下形式的双（dotsenko-fateev intemallales'）。我们替换了intemant $ \ prod | x_k | x_k |^{σ-1} \，| 1-x_k |^|^{τ-1} \ prod | x_k-x_l | x_k-x_l |^{2θ} $由复杂变量$ z_k $替换，我们整体替换，我们替换了真实变量$ x_k $ $ \ mathbb {c}^n $。根据Dotsenko，Fateev和Aomoto的说法，这种积分是伽马功能的产物。我们在空间上定义和评估一个beta积分家族$ \ mathbb {c}^m \ times \ times \ mathbb {c}^{m+1} \ times \ times \ times \ times \ times \ times \ mathbb {c}^n $
The Selberg integral has a twin (`the Dotsenko--Fateev integral') of the following form. We replace real variables $x_k$ in the integrand $\prod |x_k|^{σ-1}\,|1-x_k|^{τ-1} \prod|x_k-x_l|^{2θ}$ of the Selberg integral by complex variables $z_k$, integration over a cube we replace by an integration over the whole complex space $\mathbb{C}^n$. According to Dotsenko, Fateev, and Aomoto, such integral is a product of Gamma functions. We define and evaluate a family of beta integrals over spaces $\mathbb{C}^m\times \mathbb{C}^{m+1}\times \dots \times \mathbb{C}^n$, which for $m=n$ gives the complex twin of the Selberg integral mentioned above (with three additional integer parameters)
