Matching of Orbital Integrals on $GL(4)$ and $GSp(2)$

Released on by Yuval Zvi Flicker
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  • Matching of Orbital Integrals on $GL(4)$ and $GSp(2)$ Book Detail

  • Author : Yuval Zvi Flicker
  • Release Date : 1999
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 127
  • ISBN 13 : 0821809598
  • File Size : 36,36 MB
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Matching of Orbital Integrals on $GL(4)$ and $GSp(2)$ by Yuval Zvi Flicker PDF Summary

Book Description: The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group Sp(2). These orbital integrals are compared with those on GL(4), twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form H\ G/K--where H is a subgroup containing the centralizer--plays a key role.

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