矩阵系数关于对称空间可积性的一个判据
A criterion for integrability of matrix coefficients with respect to a symmetric space
摘要：
设$G$是约化群，$θ$是$G$上的对合，两者都定义在$p$ -adic域上.给出了$G$的表示的矩阵系数沿$θ$ -稳定抛物子群的指数的$G^θ$ -可积性的一个判据.群的情况下减少到Casselman的平方可积准则。作为一个结果，我们断言，某些家庭的对称空间是强回火的意义上的Sakellarlaughter和Venkatesh。对于其他一些家庭，我们的结果意味着所有的不可约，离散系列表示的矩阵系数是$G^θ$ -可积的。
英文摘要：
Let $G$ be a reductive group and $θ$ an involution on $G$, both defined over a $p$-adic field. We provide a criterion for $G^θ$-integrability of matrix coefficients of representations of $G$ in terms of their exponents along $θ$-stable parabolic subgroups. The group case reduces to Casselman's square-integrability criterion. As a consequence we assert that certain families of symmetric spaces are strongly tempered in the sense of Sakellaridis and Venkatesh. For some other families our result implies that matrix coefficients of all irreducible, discrete series representations are $G^θ$-integrable.
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