The Segre-Verlinde Correspondence for the Moduli Space of Stable Bundles on a Curve

We show that the classic Verlinde numbers on the moduli space \({{\textsf{M}}}(r,d)\) $\mathsf{M}(r,d)$ of rank r and degree d semistable vector bundles over a smooth projective curve can also be regarded as Segre numbers of natural universal complexes over \({{\textsf{M}}}(r,d).\) $\mathsf{M}(r,d).$ This leads to interesting identities among universal integrals on \({{\textsf{M}}}(r,d).\) $\mathsf{M}(r,d).$