The Fundamental Lemma for the Shalika Subgroup of $GL(4)$
- ISBN-10
- 0821805401
- ISBN-13
- 9780821805404
- Category
- Mathematics
- Pages
- 149
- Language
- English
- Published
- 1996
- Publisher
- American Mathematical Soc.
- Authors
- Solomon Friedberg, Herve Jacquet
Description
The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 x 2 block form ([superscript italic]g [over] [subscript capital italic]X [and] 0 [over] [superscript italic]g). The fundamental lemma, giving the equality of the orbital integrals of the unit elements of the respective Hecke algebras, amounts to a comparison of certain exponential sums arising from these two different groups.
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