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The Schwartz algebra of an affine Hecke algebra

Patrick Delorme·Eric Opdam
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Abstract

For a general affine Hecke algebra H we study its Schwartz completion S. The main theorem is an exact description of the image of S under the Fourier isomorphism. An important ingredient in the proof of this result is the definition and computation of the constant terms of a coefficient of a generalized principal series representation. Finally we discuss some consequences of the main theorem for the theory of tempered representations of H.

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Patrick Delorme, Eric Opdam. 2003-12-31. The Schwartz algebra of an affine Hecke algebra. https://arxiv.org/abs/math/0312517

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