A note on rationality of orbital integrals on a P-adic group |
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Authors: | Magdy Assem |
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Affiliation: | (1) Department of Mathematics & Statistics, University of Saskatchewan, S7N 0W0 Saskatoon, Saskatchewan, Canada |
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Abstract: | We prove that if rational measures are used on p-adic reductive groups then the orbital integrals of any given smooth and compactly supported complex valued function belong to the field generated by the values of that function. We also show that the Shalika germs are then rational valued functions. As a consequence, we are able to show, in certain cases, that the coefficients appearing in the Harish-Chandra local character expansion are rational numbers. Research supported by NSERC |
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Keywords: | 22E35 22E50 |
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