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BIRS Workshop Lecture Videos

Integrability of matrix coefficients and periods of automorphic forms Offen, Omer

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Let $G$ be a $p$-adic reductive group and $H$ a symmetric subgroup. I will present a criterion for $H$-integrability of matrix coefficients of representations of G. This is joint work with Max Gurevich and a generalization of Casselman's criteria for square integrability. Chong Zhang applied our results to show that for some symmetric subgroups all $H$-invariant linear forms of square integrable representations emerge as $H$-integrals of matrix coefficients. In particular, in a global setting, this provides information on the local components of factorizable period integrals of automorphic forms.

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