Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

TL;DR

This paper explores smooth vectors in irreducible representations of nilpotent Lie groups and discusses their application to the Weyl-Pedersen calculus for pseudo-differential operators on coadjoint orbits.

Contribution

It introduces recent results on smooth vectors and applies them to develop the Weyl-Pedersen calculus for nilpotent Lie group representations.

Findings

Characterization of smooth vectors in irreducible nilpotent Lie group representations

Application of smooth vectors to Weyl-Pedersen calculus

Development of pseudo-differential operators on coadjoint orbits

Abstract

We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.