保持连接变形与$q$ -半经典正交多项式
Connection preserving deformations and $q$-semi-classical orthogonal polynomials
摘要：
我们提出了一个研究$q$ -半经典正交系统满足的$q$ -差分方程的框架。作为一个例子，我们确定的$q$ -差分方程所满足的变形版本的小$q$ -雅可比多项式作为规范变换的一个特殊情况下的相关的线性问题的$q$ - $\mathrm{P}_{\mathrm{VI}}$。我们得到了相关的线性问题的正交多项式变量的参数化，并找到这个参数化和Jimbo和Sakai之间的关系。
英文摘要：
We present a framework for the study of $q$-difference equations satisfied by $q$-semi-classical orthogonal systems. As an example, we identify the $q$-difference equation satisfied by a deformed version of the little $q$-Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for $q$-$\mathrm{P}_{\mathrm{VI}}$. We obtain a parameterization of the associated linear problem in terms of orthogonal polynomial variables and find the relation between this parameterization and that of Jimbo and Sakai.
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