$AG_2$ Calogero-Moser-Sutherland系统的双谱性

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-11-28 DOI:10.1007/s11040-022-09440-7

Misha Feigin, Martin Vrabec

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引用次数: 1

摘要

考虑与向量组态$AG_2$相关的广义Calogero-Moser-Sutherland量子可积系统，它是根系统$A_2$和根系统$G_2$的并。我们建立了系统的存在性，构造了一个适当定义的Baker-Akhiezer函数，并证明了它满足双谱性。我们还以显式形式找到了两个对应的有理macdonald - rujsenaars型对偶差分算子。

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$Bispectrality of $AG_2$ Calogero–Moser–Sutherland System$

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Bispectrality of $AG_2$ Calogero–Moser–Sutherland System

We consider the generalised Calogero–Moser–Sutherland quantum integrable system associated to the configuration of vectors $AG_2$, which is a union of the root systems $A_2$ and $G_2$. We establish the existence of and construct a suitably defined Baker–Akhiezer function for the system, and we show that it satisfies bispectrality. We also find two corresponding dual difference operators of rational Macdonald–Ruijsenaars type in an explicit form.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.

\(AG_2\) Calogero-Moser-Sutherland系统的双谱性

摘要