The Fundamental Lemma for the Shalika Subgroup of $GL(4)$

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.