Intrinsic pseudodifferential calculi on any compact Lie group

TL;DR

This paper develops an intrinsic pseudodifferential calculus on compact Lie groups using group representations, generalizing the classical H"ormander calculus to a broader, representation-based framework.

Contribution

It introduces a new intrinsic symbolic calculus for operators on compact Lie groups, extending classical pseudo-differential theory beyond local coordinate systems.

Findings

Operators form a symbolic calculus consistent with H"ormander's on the group

The calculus is intrinsic and representation-based

Generalizes classical pseudo-differential calculus to compact Lie groups

Abstract

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which coincides or generalises the (local) H\"ormander pseudo-differential calculus on the group viewed as a compact manifold.