Volume formula for N-fold reduced products

Let G be a semisimple compact connected Lie group. An N-fold reduced product of is the symplectic quotient Hamiltonian system Cartesian N coadjoint orbits under diagonal action G. Under appropriate assumptions, it orbifold. Using technique nonabelian localization and residue formula Jeffrey Kirwan, we investigate volume an Suzuki Takakura gave for $$ \mathbf {SU}(3) in [25] by using geometric quantization Riemann–Roch formula. We compare our with theirs prove that agrees case triple products .