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arXiv · 0711.3849

Relation of Orbital Integrals on SO(5) and PGL(2)

Dmitrii Zinoviev
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Abstract

We relate the "Fourier" orbital integrals of corresponding spherical functions on the p-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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BibTeXRIS

Dmitrii Zinoviev. 2007-11-24. Relation of Orbital Integrals on SO(5) and PGL(2). https://arxiv.org/abs/0711.3849

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