Twisted Baker–Akhiezer function from determinants

IF 4.2 2区物理与天体物理 Q2 PHYSICS, PARTICLES & FIELDS

The European Physical Journal C Pub Date : 2025-05-26 DOI:10.1140/epjc/s10052-025-14297-5

A. Mironov, A. Morozov, A. Popolitov

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Abstract

General description of eigenfunctions of integrable Hamiltonians associated with the integer rays of Ding–Iohara–Miki (DIM) algebra, is provided by the theory of Chalykh Baker–Akhiezer functions (BAF) defined as solutions to a simply looking linear system. Solutions themselves are somewhat complicated, but much simpler than they could. It is because of simultaneous partial factorization of all the determinants, entering Cramer’s rule. This is a conspiracy responsible for a relative simplicity of the Macdonald polynomials and of the Noumi–Shirashi functions, and it is further continued to all integer DIM rays. Still, factorization is only partial, moreover, there are different branches and abrupt jumps between them. We explain this feature of Cramer’s rule in an example of a matrix that defines BAF and exhibits a non-analytical dependence on parameters. Moreover, the matrix is such that there is no natural expansion around non-degenerate approximations, which causes an unexpected complexity of formulas.

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来自行列式的扭曲Baker-Akhiezer函数

用Chalykh Baker-Akhiezer函数（BAF）理论给出了与Ding-Iohara-Miki （DIM）代数的整数射线相关的可积哈密顿量的特征函数的一般描述，该函数被定义为一个简单线性系统的解。解决方案本身有些复杂，但比它们所能做到的简单得多。这是因为所有行列式同时部分分解，进入克莱默法则。这是Macdonald多项式和Noumi-Shirashi函数相对简单的原因，并且它进一步适用于所有整数DIM射线。然而，因式分解只是局部的，而且它们之间存在不同的分支和突然的跳跃。我们在一个矩阵的例子中解释了克莱默规则的这一特征，该矩阵定义了BAF并表现出对参数的非解析依赖。此外，矩阵是这样的，在非退化近似周围没有自然展开，这导致了意想不到的公式复杂性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

The European Physical Journal C 物理-物理：粒子与场物理

CiteScore

8.10

自引率

15.90%

发文量

1008

审稿时长

2-4 weeks

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