Bundles of rank 3 on curves of Clifford index 3

Two definitions of the Clifford index for vector bundles on a smooth projective curve $C$ of genus $g\ge 4$ were introduced in a previous paper by the authors. In another paper the authors obtained results on one of these indices for bundles of rank 3. In this paper we extend these results in the case where $C$ has classical Clifford index 3. In particular we prove Mercat’s conjecture for bundles of rank 3 for $g\le 8$ and $g\ge 13$ when $C$ has classical Clifford index 3. We obtain complete results in the case of genus 7.