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On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions , 2023статья
- Автор: Neretin Yu A.
- Журнал: Ramanujan Journal
- Год издания: 2023
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- DOI: 10.1007/s11139-023-00804-3
- Аннотация: The Selberg integral has a twin (`the Dotsenko--Fateev integral')of the following form. We replace real variables $x_k$ in the integrand $\prod |x_k|^{\sigma-1}\,|1-x_k|^{\tau-1} \prod|x_k-x_l|^{2\theta}$ of the Selbergintegral by complex variables $z_k$, integration over a cube we replace by an integration over the wholecomplex 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 ofthe Selberg integral mentioned above (with three additional integer parameters).
- Добавил в систему: Неретин Юрий Александрович