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 L 2 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 and Pal for SU q (2).