A criterion for integrability of matrix coefficients with respect to a symmetric space
A criterion for integrability of matrix coefficients with respect to a symmetric space
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DOI：
10.1016/j.jfa.2016.02.008
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
M. Gurevich;Omer Offen
中科院分区：
文献类型：
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作者：
M. Gurevich;Omer Offen
设G是一个约化群，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沿着θ-稳定抛物子群的指数G θ-可积的一个判别准则.群的情形归结为卡塞尔曼的平方可积准则。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。对于其他一些族，我们的结果意味着所有不可约的离散级数表示的矩阵系数是G θ-可积的。
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.