On Rational Nilpotent Orbits of $SL_{n}$ and $Sp_{2n}$ over a Local Non-Archimedean Field
Abstract
Description
We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the split classical groups $SL_n$ and $Sp_{2n}$ over local non-Archimedean fields with a parametrization, introduced by DeBacker in 2002, which uses the associated Bruhat-Tits building to relate the question to one over the residue field.
v2, 27 pages. Reduced to single-spacing (from double-spaced first version of 35 pages); typos corrected in Section 2; Corollary 4.5 strengthened
v2, 27 pages. Reduced to single-spacing (from double-spaced first version of 35 pages); typos corrected in Section 2; Corollary 4.5 strengthened