Authors: Avraham Aizenbud Dmitry Gourevitch Siddhartha Sahi
Publish Date: 2015/02/20
Volume: 206, Issue: 1, Pages: 1-38
Abstract
The notion of derivatives for smooth representations of GLn ℚ p was defined in BZ77 In the archimedean case an analog of the highest derivative was defined for irreducible unitary representations in Sah89 and called the “adduced” representation In this paper we define derivatives of all orders for smooth admissible Fréchet representations of moderate growth The real case is more problematic than the padic case for example arbitrary derivatives need not be admissible However the highest derivative continues being admissible and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representationWe apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations thus completing the results of Sah89 Sah90 SaSt90 GS13a
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