Why Whittaker functions are useful?

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reference help on a result of Whittaker functions of supercuspidal representations

Let $F$ be a p-adic field, $\pi$ an irreducible supercuspidal representation of $GL(n,F)$, then it admits a unique Whittaker model $\mathcal{W}(\pi)$. For any $W\in \mathcal{W}(\pi)$, a basic result is that $W(g)$ is a compactly supported function mod $NZ$, where $N$ is the maximal unipotent subgroup and $Z$ is the center of $GL(n,F)$. Does anyone know a reference containing this result? Many thanks.

Answer:

I think this can be seen directly. Let's work over $G=PGL(n)$, so I don't have to keep repeating "...

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user1832 at Mathoverflow Mark as irrelevant Undo

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