Abstract
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.
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