rujsenaars双曲系统中的Baxter算子II:双谱波函数

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2023-11-20 DOI:10.1007/s00023-023-01385-z

N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin

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引用次数: 0

摘要

在上一篇论文中，我们引入了量子rujsenaars双曲系统的交换Baxter q算子族。在目前的工作中，我们证明了M. Hallnäs和S. rujsenaars发现的量子系统的波函数也对角化Baxter算子。利用这一性质，证明了波函数的猜想对偶关系。作为推论，我们证明了波函数解决了对偶Macdonald和Baxter算子对的双谱问题。此外，我们证明了波函数关于谱变量的猜想对称性，并得到了波函数关于谱变量的新的积分表示。

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Baxter operators in Ruijsenaars hyperbolic system II: bispectral wave functions

In the previous paper, we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work, we show that the wave functions of the quantum system found by M. Hallnäs and S. Ruijsenaars also diagonalize Baxter operators. Using this property, we prove the conjectured duality relation for the wave function. As a corollary, we show that the wave function solves bispectral problems for pairs of dual Macdonald and Baxter operators. Besides, we prove the conjectured symmetry of the wave function with respect to spectral variables and obtain new integral representation for it.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.