A canonical dimension estimate for non-split semisimple p-adic Lie groups

TL;DR

This paper establishes a lower bound for the canonical dimension of certain representations of semisimple p-adic Lie groups, extending previous results from split to arbitrary cases, with implications for understanding their structure.

Contribution

It generalizes the canonical dimension estimates from split to non-split semisimple p-adic Lie groups, broadening the scope of previous work.

Findings

Canonical dimension is either zero or at least half the dimension of a non-zero coadjoint orbit.

Extends previous results from split to arbitrary semisimple p-adic Lie groups.

Provides a new lower bound for the canonical dimension of admissible Banach space or locally analytic representations.

Abstract

We prove that the canonical dimension of an admissible Banach space or a locally analytic representation of an arbitrary semisimple p-adic Lie group is either zero or at least half the dimension of a non-zero coadjoint orbit. This extends the results of Ardakov-Wadsley and Schmidt in the split semisimple case.