On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on p-adic Symplectic Groups.

Intro -- Contents -- 0. Introduction -- 1. Unipotent orbits and prehomogeneous spaces -- 1. Ranga Rao data -- 2. Some classes of examples -- 3. Induction of G(F)-unipotent classes -- 2. The Hecke algebra and some Igusa local orbital zeta functions -- 1. Unipotent orbital integrals as special values of orbital Igusa zeta functions -- 2. GL(n,O[sub(F))]-orbit decomposition of Sym (n) and local densitites -- 3. The K-decomposition of supp (X [omitted] f[sub(m)](1 + X)) ∩ g(2) -- 3. The evaluation of f[sup(H)] at the identity -- 1. The integral of Φ[sub(k)], 2 ≤ k ≤ n, Part A -- 2. The integral of Φ[sub(k)], 2 ≤ k ≤ n, Part B -- 3. The integral of Φ[sub(1)] -- 4. The value f[sup(H) (1))] for H = SO[sup(E) (4) x SL(2) -- 5. Matching results -- 4. Matching of unipotent orbital integrals -- 1. Unramified endoscopic data -- 2. The map f [omitted] f[sup(H) -- 3. Endoscopic induction of unipotent orbits -- 4. Matching of regular unipotent orbital integrals -- 5. Matching of unipotent orbital integrals for G = Sp(6) and its unramified endoscopic groups -- 6. Matching of subregular orbital integrals -- 7. Matching of the orbits 2[sup(r)] 1[sup(2n-2r)], for r = 2,3 -- 8. Matching results for Sp(8) -- 9. Endoscopic transfer of the trivial orbital integral -- 10. Endoscopic transfer of other orbital integrals -- 11. Some remarks on the transfer factors -- 5. Remarks on stability and endoscopic transfer -- 1. Stable distributions -- 2. Formal properties of endoscopic induction and stability -- 3. Remarks on Shalika germs -- 4. Conjecture (B) implies Conjecture (A) -- 5. Stability and subregular packets -- 6. Heuristics -- Appendix I -- Appendix II -- References.

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