Tokyo Journal of Mathematics

Symplectic Volumes of Certain Symplectic Quotients Associated with the Special Unitary Group of Degree Three

Taro SUZUKI and Tatsuru TAKAKURA

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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.

Article information

Tokyo J. Math., Volume 31, Number 1 (2008), 1-26.

First available in Project Euclid: 27 August 2008

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Zentralblatt MATH identifier

Primary: 53D20: Momentum maps; symplectic reduction
Secondary: 22E46: Semisimple Lie groups and their representations


SUZUKI, Taro; TAKAKURA, Tatsuru. Symplectic Volumes of Certain Symplectic Quotients Associated with the Special Unitary Group of Degree Three. Tokyo J. Math. 31 (2008), no. 1, 1--26. doi:10.3836/tjm/1219844821.

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