Induction for locally compact quantum groups revisited

TL;DR

This paper revisits the theory of induced representations for locally compact quantum groups, showing equivalences between different constructions and establishing continuity properties.

Contribution

It demonstrates the equivalence of Kustermans and Vaes' induction with Rieffel's classical construction for open quantum subgroups and proves the continuity of induction in the general setting.

Findings

Equivalence of induction constructions for open quantum subgroups

Continuity of induction with respect to weak containment

Simplification of induction theory in quantum groups

Abstract

In this paper we revisit the theory of induced representations in the setting of locally compact quantum groups. In the case of induction from open quantum subgroups, we show that constructions of Kustermans and Vaes are equivalent to the classical, and much simpler, construction of Rieffel. We also prove in general setting the continuity of induction in the sense of Vaes with respect to weak containment.