Characterization of spectral triples: A combinatorial approach

We describe a general technique to study Dirac operators on noncommutative spaces under some additional assumptions. The main idea is to capture the compact resolvent condition in a combinatorial set up. Using this, we then prove that for a certain class of representations of the C^*-algebra C(SU_q(\ell+1)), any Dirac operator that diagonalises with respect to the natural basis of the underlying Hilbert space must have trivial sign.