Explicit Rieffel induction module for quantum groups

Damien Rivet (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

For G an algebraic (or more generally, a bornological) quantum group and B a closed quantum subgroup of G, we build in this paper an induction module by explicitly defining an inner product which takes its value in the convolution algebra of B, as in the original approach of Rieffel [Rie74]. In this context, we study the link with the induction functor defined by Vaes. In the last part we illustrate our result with parabolic induction of complex semi-simple quantum groups with the approach suggested by Clare [Cla13][CCH16].

Mots clés: quantum groups; representation theory; complex semi-simple groups; parabolic induction; Hilbert modules

Domaines: Mathématiques [math]; Algèbres quantiques [math.QA]; Algèbres d'opérateurs [math.OA]

Damien Rivet. Explicit Rieffel induction module for quantum groups. 2019. ⟨hal-02347447⟩