Special function models of indecomposable sl(2) representations: the Laguerre case

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-07-29 DOI:10.1088/1751-8121/ad653c
Sébastien Bertrand, Ian Marquette, Willard Miller, Sarah Post
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Abstract

In this paper, we point out connections between certain types of indecomposable representations of sl(2) and generalizations of well-known orthogonal polynomials. Those representations take the form of infinite dimensional chains of weight or generalised weight spaces, for which the Cartan generator acts in a diagonal way or via Jordan blocks. The other generators of the Lie algebras sl(2) act as raising and lowering operators but are now allowed to relate the different chains as well. In addition, we construct generating functions, we calculate the action of the Casimir invariant and present relations to systems of non-homogeneous second-order coupled differential equations. We present different properties as higher-order linear differential equations for building blocks taking the form of one variable polynomials. We also present insight into the zeroes and recurrence relations.
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不可分解 sl(2) 表示的特殊函数模型:拉盖尔案例
在本文中,我们指出了 sl(2) 的某些不可分解表示类型与著名的正交多项式广义化之间的联系。这些表示形式为无限维的权重链或广义权重空间,其中 Cartan 发生器以对角方式或通过约旦块起作用。而列代数 sl(2) 的其他生成器则充当提升和降低运算符,但现在也可以将不同的链联系起来。此外,我们还构建了生成函数,计算了卡西米尔不变量的作用,并提出了非均质二阶耦合微分方程系统的关系。我们为一变多项式形式的构件提出了高阶线性微分方程的不同性质。我们还介绍了零点和递推关系。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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