Local periods for discrete series representations

Let $(G,H)$ be a symmetric pair over a $p$-adic field and $π$ a discrete series representation of $G$. In this paper, for some type of symmetric pairs $(G,H)$, we show that local periods in $Hom_H(π,\mathbb{C})$ can be constructed by integrating the matrix coefficients of $π$ over $H$.

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