The volume of the N-fold reduced product of coadjoint orbits

TL;DR

This paper calculates the symplectic volume of the reduced space formed by N coadjoint orbits of a compact Lie group, extending previous work by Suzuki and Takakura for SU(3).

Contribution

It provides a general computation of symplectic volumes for N-fold products of coadjoint orbits, broadening understanding beyond specific cases.

Findings

Explicit formula for symplectic volume of reduced space

Comparison with previous results for SU(3)

Extension to general compact Lie groups

Abstract

We compute the symplectic volume of the symplectic reduced space of the product of N coadjoint orbits of a compact connected Lie group G. We compare our result with the result of Suzuki and Takakura , who study this in the case G = SU(3) starting from geometric quantization.