A formula for certain intersection number on q-Hamiltonian reduced space

In this paper, we derive a formula for the intersection number of certain characteristic classes on [Formula: see text]-Hamiltonian reduced space, which are related to curvature of principle bundle. Moreover, such intersection number can also be expressed in the term of differential operators acting on the symplectic volume of nearby reduced space. As an application, we give a new proof of an important step in Bismut and Labourie’s proof of Verlinde formula.