English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is animportant and non-trivial example of a non-compact quantum group. The generaltheory of locally compact quantum groups in the operator algebra settingimplies the existence of the dual quantum group. The first main goal of thepaper is to give an explicit description of the dual quantum group for thisexample involving the quantized enveloping algebra U_q(su(1,1)). It turns outthat U_q(su(1,1)) does not suffice to generate the dual quantum group. The dualquantum group is graded with respect to commutation and anticommutation with asuitable analogue of the Casimir operator characterized by an affiliationrelation to a von Neumann algebra. This is used to obtain an explicit set ofgenerators. Having the dual quantum group the left regular corepresentation ofthe quantum group analogue of the normalizer of SU(1,1) in SL(2,C) isdecomposed into irreducible corepresentations. Upon restricting the irreduciblecorepresentations to U_q(su(1,1))-representation one finds combinations of thepositive and negative discrete series representations with the strange seriesrepresentations as well as combinations of the principal unitary seriesrepresentations. The detailed analysis of this example involves analysis ofspecial functions of basic hypergeometric type and, in particular, some resultson these special functions are obtained, which are stated separately.  The paper is split into two parts; the first part gives almost all of thestatements and the results, and the statements in the first part areindependent of the second part. The second part contains the proofs of all thestatements.

The dual quantum group for the quantum group analogue of the normalizer of SU(1,1) in SL(2,C)