A special value of the spectral zeta function of the non-commutative harmonic osciallators

非交换谐振子与双光子量子Rabi模型的等价性

Equivalence between non-commutative harmonic oscillators and two-photon quantum Rabi models

本文证明了非交换谐振子、双光子量子Rabi模型及单位圆盘上的全纯微分方程三者之间的等价性，并探讨了合流过程及与单光子模型的关系。

$\mathfrak{sl}(2,\mathbb{R})\simeq \mathfrak{su}(1,1)$ 的表示理论与非交换谐振子的推广

Representation theory of $\mathfrak{sl}(2,\mathbb{R})\simeq \mathfrak{su}(1,1)$ and a generalization of non-commutative harmonic oscillators

本文利用李代数表示理论，将非交换谐振子推广至高维旋转不变情形，证明其特征值问题可化为单位圆盘上的富克斯型全纯微分方程。

Some harmonic analysis on commutative nilmanifolds

In this work, we consider a family of Gelfand pairs $(K \ltimes N, N)$ (in short $(K,N)$) where $N$ is a two step nilpotent Lie group, and $K$ is the group of orthogonal automorphisms of $N$. This family has a nice analytic property: almost all these 2-step nilpotent Lie group have square integrable representations. In this cases, following Moore-Wolf's theory, we find an explicit expression for the inversion formula of $N$, and as a consequence, we decompose the regular action of $K \ltimes N$ on $L^{2}(N)$. This result completes the analysis carried out by Wolf, where the inversion formula i…