Towards an orbit method for nilpotent Lie groupoidsOberseminar Global Analysis and Operator Algebras

by Foteini Giapantzi (Uni Bonn)

Tuesday Jun 16, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60/1-008 (Mathezentrum)

Kirillov's orbit method establishes a correspondence between irreducible unitary representations of connected, simply connected nilpotent Lie groups and their coadjoint orbits. This correspondence plays a central role in representation theory and has important applications in analysis, including the study of hypoelliptic differential operators.

In this talk, I will review the classical orbit method for nilpotent Lie groups and discuss its extension to transformation-group $C^*$-algebras, as introduced by Dean Moore. This result describes the primitive ideal space of $C^*(G,\Omega)$ in terms of a quotient of $\mathfrak{g}^* \times \Omega$. Finally, I will introduce Lie groupoids and discuss the question of whether an orbit-method framework can be developed for suitable classes of nilpotent Lie groupoids.