On Rational Nilpotent Orbits of $S{L}_n$ and $S{p}_{2n}$ over a Local Non-Archimedean Field

Abstract

We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the split classical groups $S{L}_n$ and $S{p}_{2n}$ 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

References in corpus (1)

• Nilpotent orbits over ground fields of good characteristic