Relation of orbital integrals on SO(5) and PGL(2) |
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Authors: | Dmitrii Zinoviev |
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Affiliation: | (1) Department of Mathematics, The Ohio State University, 231 W. 18th Ave., 43210 Columbus, OH, USA |
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Abstract: | We relate the “Fourier” orbital integrals of corresponding spherical functions on thep-adic groups SO(5) and PGL(2). The correspondence is defined by a “lifting” of representations of these groups. This is a local “fundamental lemma” needed to compare the geometric sides of the global Fourier summation formulae (or relative trace formulae) on these two groups. This comparison leads to conclusions about a well known lifting of representations from PGL(2) to PGSp(4). This lifting produces counter examples to the Ramanujan conjecture. |
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