Characterization of $S{U}_q(\ell +1)$-equivariant spectral triples for the odd dimensional quantum spheres

Abstract

The quantum group $S{U}_q(\ell +1)$ has a canonical action on the odd dimensional sphere $S_q^{2\ell +1}$. All odd spectral triples acting on the $L_2$ space of $S_q^{2\ell +1}$ 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 $S{U}_q(2)$.

LaTeX2e, 20 pages