论文标题
（$ q $ - ）线性网格和（$ q $ - ）para-krawtchouk多项式（$ q $ - ）类似Sklyanin的代数
Sklyanin-like algebras for ($q$-)linear grids and ($q$-)para-Krawtchouk polynomials
论文作者
论文摘要
引入了线性和$ Q $ - 线性网格的S-Heun运营商。这些操作员是Heun操作员的特殊情况，与Sklyanin样代数有关。连续的Hahn和Big Q $ -Jacobi多项式是这些S-Heun运营商具有自然作用的功能。我们表明，S-Heun运营商包括双光谱运营商和Kalnins和Miller的结构操作员。这四个结构操作员意识到原始Sklyanin代数的三角变性的特殊限制案例。这些代数的有限维表示是从截断条件获得的。相应的表示基础是多项式的有限族：para-krawtchouk和$ q $ -para-krawtchouk。因此，获得了对这些多项式的自然代数解释。我们还恢复了附属于相应双光谱问题的HEUN操作员，作为S-Heun操作员的二次组合
S-Heun operators on linear and $q$-linear grids are introduced. These operators are special cases of Heun operators and are related to Sklyanin-like algebras. The Continuous Hahn and Big $q$-Jacobi polynomials are functions on which these S-Heun operators have natural actions. We show that the S-Heun operators encompass both the bispectral operators and Kalnins and Miller's structure operators. These four structure operators realize special limit cases of the trigonometric degeneration of the original Sklyanin algebra. Finite-dimensional representations of these algebras are obtained from a truncation condition. The corresponding representation bases are finite families of polynomials: the para-Krawtchouk and $q$-para-Krawtchouk ones. A natural algebraic interpretation of these polynomials that had been missing is thus obtained. We also recover the Heun operators attached to the corresponding bispectral problems as quadratic combinations of the S-Heun operators
