Comparison of germ expansion on inner forms of GL(n)

Prasad, Dipendra (2000) Comparison of germ expansion on inner forms of GL(n) Manuscripta Mathematica, 102 (2). pp. 263-268. ISSN 0025-2611

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Related URL: http://dx.doi.org/10.1007/s002291020263

Abstract

We prove that the germ expansion of a discrete series representation π' on GLn(D) where D is a division algebra over k of index m and the germ expansion of the representation π of GLmn(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 GLmn(k) can be interpreted (and therefore sometimes calculated) in terms of the dimension of a certain space of (degenerate) Whittaker models on GLn(D).

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