不可约酉表示的近帕塞瓦尔轨道框架：来自混合与展开
Near-Parseval orbit frames for irreducible unitary representations: from mixing and expansion
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中文总结 AI 辅助
该研究针对带共轭逃逸单参数子群的射影C₀酉表示建立抽象存储定理，生成满足特定框架界的轨道框架，应用于指数李群的左正则表示及不可约酉表示，得出非阿贝尔指数李群为FT群等结论。
中文摘要 AI 辅助
我们针对具有一对带共轭逃逸的单参数子群的射影C₀酉表示，建立了一个抽象存储定理。该定理对每个0<ε<1，生成一个单一轨道，其采样集相对于射影核是相对分离的，且框架界为(1−ε)²和(1+ε)²。从同一机制得到两个应用：第一，每个非阿贝尔指数李群对其左正则表示都存在左平移构成的近帕塞瓦尔框架，因此正维指数李群是FT群当且仅当它是非阿贝尔的，特别地，三维海森堡群存在此类框架；第二，指数李群的每个无限维不可约酉表示都存在近帕塞瓦尔离散轨道框架，当有效射影商为阿贝尔时，该轨道可选取为来自迁移外尔格的正交基。
英文摘要
We establish an abstract storage theorem for projectively $C_0$ unitary representations admitting a pair of one-parameter subgroups with conjugation escape. It produces, for every $0<\varepsilon<1$, a single orbit whose sampling set is relatively separated modulo the projective kernel and whose frame bounds are $(1-\varepsilon)^2$ and $(1+\varepsilon)^2$. Two applications are obtained from the same mechanism. First, every nonabelian exponential Lie group admits a near-Parseval frame of left translates for its left regular representation. Consequently, a positive-dimensional exponential Lie group is an FT group if and only if it is nonabelian; in particular, the three-dimensional Heisenberg group admits such a frame. Second, every infinite-dimensional irreducible unitary representation of an exponential Lie group admits a near-Parseval discrete orbit frame. When the effective projective quotient is abelian, the orbit may be chosen to be an orthonormal basis arising from a transported Weyl lattice.
