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June 2008 Symplectic Volumes of Certain Symplectic Quotients Associated with the Special Unitary Group of Degree Three
Taro SUZUKI, Tatsuru TAKAKURA
Tokyo J. Math. 31(1): 1-26 (June 2008). DOI: 10.3836/tjm/1219844821

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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Taro SUZUKI. Tatsuru TAKAKURA. "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

Information

Published: June 2008
First available in Project Euclid: 27 August 2008

zbMATH: 1157.53045
MathSciNet: MR2426792
Digital Object Identifier: 10.3836/tjm/1219844821

Subjects:
Primary: 53D20
Secondary: 22E46

Rights: Copyright © 2008 Publication Committee for the Tokyo Journal of Mathematics

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Vol.31 • No. 1 • June 2008
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