Induction for representations of coideal doubles, with an application to quantum $SL(2,\mathbb{R})$

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 $SL(2,\mathbb{R})$, and compute the decomposition of the regular representation for quantum $SL(2,\mathbb{R})$ into irreducibles.

35 pages; Section 5 substantially rewritten; Theorem 5.13 corrects the inaccurate statement in Theorem 5.11 of the previous version (an exceptional case was overlooked). Accepted version, to be published in Indigationes Mathematicae