Characterization of SU_q(l+1)-equivariant spectral triples for the odd dimensional quantum spheres

Abstract

The quantum group SU_q(l+1) has a canonical action on the odd dimensional sphere S_q^2l+1. All odd spectral triples acting on the L₂ space of S_q^2l+1 and equivariant under this action have been characterized. This characterization then leads to the construction of an optimum family of equivariant spectral triples having nontrivial K-homology class. These generalize the results of Chakraborty & Pal for SU_q(2).