Fundamental solutions of invariant differential operators on a semisimple Lie group II

Guillermo Ames

Vol. 207 (2002), No. 1, 1–11

DOI: 10.2140/pjm.2002.207.1

Abstract

Let G be a linear connected semisimple Lie group. We denote by 𝒰(g)^K the algebra of left invariant differential operators on G that are also right invariant by K, and 𝒵(𝒰(g)^K) denotes center of 𝒰(g)^K.

In this paper we give a sufficient condition for a differential operator P ∈𝒵(𝒰(g)^K) to have a fundamental solution on G. This result extends the same one obtained previously for real rank one Lie groups and groups with only one conjugacy class of Cartan subgroups.

Milestones

Received: 1 March 2001

Revised: 30 May 2001

Published: 1 November 2002