约旦量子群SL_h（2）的表示函数与雅可比多项式

Little and Big $q-$Jacobi Polynomials and the Askey-Wilson algebra

The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey-Wilson algebra generated by twisted primitive elements of $\mathfrak U_q(sl(2))$. The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey-Wilson algebra into $\mathfrak U_q(sl(2))$.

Jacobi operator, q-difference equation and orthogonal polynomials

In this paper, a link between $q$-difference equations, Jacobi operators and orthogonal polynomials is given. Replacing the variable $x$ by $ q^{-n}$ in a Sturm-Liouville $q$-difference equation we discovered the Jacobi operator. With appropriate initial conditions, the eigenfunctions of such operators are either $q$-orthogonal polynomials or the modified $q$-Bessel function and a newborn the $q$-Macdonald ones. The new Polynomial sequence we found is related to the $q$-Lommel polynomials introduced by Koelink and other. Adapting E. C. Titchmarsh's theory, we showed the existence of a solution…

关于q-正交多项式与小、大q-雅可比多项式的对偶

On q-orthogonal polynomials, dual to little and big q-Jacobi polynomials

本文利用量子代数U_q（su_{1,1}）的离散级数表示的算子，研究了q-雅可比多项式及其多项式的性质.这些运营商的频谱和本征函数被发现明确。这些本征函数在归一化时形成表示空间中的正交基。初始U_q（su_{1,1}）基和这些特征函数的基由矩阵连接，矩阵的元素用小q和大q-雅可比多项式表示.这些酉联络矩阵的行正交性导致了小q-雅可比多项式和大q-雅可比多项式的正交关系。利用联络矩阵的列正交性，得到了分别与大、小q-雅可比多项式对偶的{}_3 <$_2和{}_3 <$_1多项式在可数点集上的正交关系的显式表示。证明了对偶小q-雅可比多项式的正交性测度是极值的，而对偶大q-雅可比多项式的正交性测度不是极值的.

量子超球及其变换群、表示和小$t$ -雅可比多项式

Quantum super spheres and their transformation groups, representations, and little $t$-Jacobi polynomials

引入了量子超2-球面和相应的量子超变换群，建立了小$t$ -雅可比多项式与量子超群的有限维表示之间的关系，得到了Peter-Weyl定理.

Jacobi三重积和Lebesgue恒等式的新多项式模拟

New polynomial analogues of Jacobi's triple product and Lebesgue's identities

在作者最近的一篇论文中，建立了Goellnitz（大）划分定理的有界版本。在这里，我们将展示除其他事项外，这一定理如何导致非平凡的新的多项式类似物的某些基本身份的雅可比和勒贝格。我们还推导出了Jacobi著名的三重积恒等式的一个两参数的推广。

BC-infinity Calogero-Moser operator and super Jacobi polynomials

An infinite-dimensional version of Calogero-Moser operator of $BC$-type and the corresponding Jacobi symmetric functions are introduced and studied, including the analogues of Pieri formula and Okounkov's binomial formula. We use this to describe all the ideals linearly generated by the Jacobi symmetric functions and show that the deformed $BC(m,n)$ Calogero-Moser operators, introduced in our earlier work, appear here in a natural way as the restrictions of the $BC_{\infty}$ operator to the corresponding finite-dimensional subvarieties. As a corollary we have the integrability of these quantum…