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I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.
In this paper, Shintani proves the Casselman-Shalika(-Shintani) formula for GL(n). This preceded Casselman-Shalika's paper by a few years. Several of Cogdell's expository articles on L-functions have easy-to-read descriptions of the formula.
Required, but never shown