局部对称空间上的量子唯一遍历性：退化提升
Quantum unique ergodicity on locally symmetric spaces: the degenerate lift
摘要：
给定局部对称空间$Y=Γ\backslash G/K$上的测度$\barμ$，作为与不变微分算子环的本征函数相关联的概率测度的弱{*}极限，我们在齐性空间$X=Γ\backslash G$上构造了一个测度$μ$，它提升了$\barμ$，并且对于正维的连通子群$A_{1}\subset A$是不变的，其中$G=NAK$是Iwasawa分解.此外，如果函数是Hecke算子的本征函数，则$μ$也是与$X$上的Hecke本征函数相关的度量的极限。这推广了作者和A. Venkatesh的情况下，“退化”的限制光谱参数。
英文摘要：
Given a measure $\barμ$ on a locally symmetric space $Y=Γ\backslash G/K$, obtained as a weak-{*} limit of probability measures associated to eigenfunctions of the ring of invariant differential operators, we construct a measure $μ$ on the homogeneous space $X=Γ\backslash G$ which lifts $\barμ$ and which is invariant by a connected subgroup $A_{1}\subset A$ of positive dimension, where $G=NAK$ is an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, then $μ$ is also the limit of measures associated to Hecke eigenfunctions on $X$. This generalizes previous results of the author and A.\ Venkatesh to the case of "degenerate" limiting spectral parameters.
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