关于球面簇酉谱的Sakellaridis-Venkatesh猜想
A Conjecture of Sakellaridis-Venkatesh on the Unitary Spectrum of Spherical Varieties
摘要：
在最近的预印本中，Sakellaridis和Venkatesh考虑了空间$L^2(X)$的谱分解，其中$X = H\G$是球形簇，$G$是实群或$p$-adic群，并陈述了一个猜想，根据与$X$相关的对偶群$\check{G}_X$描述了这种分解。本文的主要目的是在$X$，具有低秩的情况下，在许多情况下验证上述猜想。特别是，我们证明了这个猜想的许多情况下，当$X$有秩1，也有一些情况下，当$X$有秩2或3。
英文摘要：
In a recent preprint, Sakellaridis and Venkatesh considered the spectral decomposition of the space $L^2(X)$, where $X = H\G$ is a spherical variety and $G$ is a real or $p$-adic group, and stated a conjecture describing this decomposition in terms of a dual group $\check{G}_X$ associated to $X$. The main purpose of this paper is to verify the above conjecture in many cases when $X$, has low rank. In particular, we demonstrate this conjecture for many cases when $X$ has rank 1, and also some cases when $X$ has rank 2 or 3.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
