Tokyo Journal of Mathematics

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

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.

Article information

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

Dates
First available in Project Euclid: 27 August 2008

https://projecteuclid.org/euclid.tjm/1219844821

Digital Object Identifier
doi:10.3836/tjm/1219844821

Mathematical Reviews number (MathSciNet)
MR2426792

Zentralblatt MATH identifier
1157.53045

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

Citation

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. https://projecteuclid.org/euclid.tjm/1219844821

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