Induction for representations of coideal doubles, with an application to quantum SL(2,R)

Abstract

We investigate the theory of induction in the setting of doubles of coideal $\ast$-subalgebras of compact quantum group Hopf $\ast$-algebras. We then exemplify parts of this theory in the particular case of quantum $SL(2,R)$, and compute the decomposition of the regular representation for quantum $SL(2,R)$ into irreducibles.