作为模块组矩阵系数的鲁伊塞纳斯波函数

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-11-27 DOI:10.1007/s11005-024-01881-1

Philippe Di Francesco, Rinat Kedem, Sergey Khoroshkin, Gus Schrader, Alexander Shapiro

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引用次数: 0

摘要

我们以作用于穿刺环上的 GL(2) 量子 Teichmüller 理论的希尔伯特空间的 4 阶元素 \(S\in SL(2,{\mathbb {Z}})\) 的矩阵系数来描述 2 粒子双曲 Ruijsenaars 系统的 Hallnäs-Ruijsenaars 特征函数。然后，GL(2) 麦克唐纳多项式就可以作为这些矩阵系数的解析延续的特殊值而得到。证明中使用的主要工具是穿刺环上有框 GL(2) 局部系统模空间上的簇结构，以及 GL(2) 球面 DAHA 到相应簇泊松数的量化坐标环的\(SL(2,{\mathbb {Z}})\)-后向嵌入。

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Ruijsenaars wavefunctions as modular group matrix coefficients

We give a description of the Hallnäs–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element \(S\in SL(2,{\mathbb {Z}})\) acting on the Hilbert space of GL(2) quantum Teichmüller theory on the punctured torus. The GL(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framed GL(2)-local systems on the punctured torus, and an \(SL(2,{\mathbb {Z}})\)-equivariant embedding of the GL(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.