On Kostant Sections and Topological Nilpotence
Representation Theory
2019-03-13 v2 Number Theory
Abstract
Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks out a G(F)-conjugacy class in every stable, regular, topologically nilpotent conjugacy class in g(F). This generalizes an earlier result obtained by DeBacker and one of the authors under stronger hypotheses. We then show that if F is p-adic, then the characteristic function of this set behaves well with respect to endoscopic transfer.
Cite
@article{arxiv.1611.08566,
title = {On Kostant Sections and Topological Nilpotence},
author = {Jeffrey D. Adler and Jessica Fintzen and Sandeep Varma},
journal= {arXiv preprint arXiv:1611.08566},
year = {2019}
}
Comments
23 pages, accepted for publication in the Journal of the London Mathematical Society