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I would like to know some nice references about the relation between asymptotics of matrix coefficients of representations of reductive groups over local fields, and the pairing between the Jacquet module of the representation and the Jacquet module of its dual.

I would like to know reference for the p-adic case, as well as for the real case (where one uses Jacquet-Casselmann functor instead of Jacquet functor).

As I understand, both cases are due to Casselmann.

Thank you, Sasha

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Have you looked at Casselman's papers on this? There are four papers to look at, the three with "asymptotic" in their title and his original notes on representations of $p$-adic groups. You can also find Casselman's ICM paper, "Jacquet Modules for Real Reductive Groups", online. Wallach's book, "Real Reductive Groups I", also has material. – B R Mar 6 '12 at 16:18
Thank you for the references! – Sasha Mar 6 '12 at 19:11

For real groups, You find a precise answer to your question in the work of Hecht Henryk and Wilfried Schmid, best regards jorge

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