论文标题
指数晶格上的离散正交合奏
Discrete orthogonal ensemble on the exponential lattices
论文作者
论文摘要
受Aomoto的$ Q $ -Selberg Integral的启发，本文考虑了指数晶格中的正交合奏。通过引入偏斜的对称内核，该集合的配置空间被构造为对称，因此，相应的偏斜内部产物，偏斜正交多项式以及相关函数被明确提出。考虑了包括Al-Salam＆Carlitz，$ Q $ -Laguerre，Little $ Q $ -Jacobi和Big Q $ -Jacobi案件在内的示例。
Inspired by Aomoto's $q$-Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and thus, corresponding skew inner product, skew orthogonal polynomials as well as correlation functions are explicitly formulated. Examples including Al-Salam & Carlitz, $q$-Laguerre, little $q$-Jacobi and big $q$-Jacobi cases are considered.
