We consider the symplectic quotient for a direct product of several integral coadjoint orbits of $SU(3)$ and investigate its symplectic volume. According to a fundamental theorem for symplectic quotients, it is equivalent to studying the dimension of the trivial part in a tensor product of several irreducible representations for $SU(3)$, and its asymptotic behavior. We assume that either all of coadjoint orbits are flag manifolds of $SU(3)$, or all are complex projective planes. As main results, we obtain an explicit formula for the symplectic volume in each case.
"Symplectic Volumes of Certain Symplectic Quotients Associated with the Special Unitary Group of Degree Three." Tokyo J. Math. 31 (1) 1 - 26, June 2008. https://doi.org/10.3836/tjm/1219844821