Abstract
We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots. As a consequence, there is either a unique set, or an (almost) unique two-parameter set of Weyl group invariant quantum zonal spherical functions associated to an irreducible symmetric pair. Included is a complete and explicit list of the generators and relations for the left coideal subalgebras of the quantized enveloping algebra used to form quantum symmetric pairs.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Letzter, G. Quantum Symmetric Pairs and Their Zonal Spherical Functions. Transformation Groups 8, 261–292 (2003). https://doi.org/10.1007/s00031-003-0719-9
Issue Date:
DOI: https://doi.org/10.1007/s00031-003-0719-9