Comparison of germ expansion¶on inner forms of GL(n)
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We prove that the germ expansion of a discrete series representation π′ on GL n (D) where D is a division algebra over k of index m and the germ expansion of the representation π of GL mn (k) associated to π′ by the Deligne–Kazhdan–Vigneras correspondence are closely related, and therefore certain coefficients in the germ expansion of a discrete series representation of GL mn (k) can be interpreted (and therefore sometimes calculated) in terms of the dimension of a certain space of (degenerate) Whittaker models on GL n (D).
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