Volume Formula and Intersection Pairings of N-fold Reduced Products

Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an N-fold reduced product of G. In 2008, Suzuki and Takakura gave a volume formula of N-fold reduced products of SU(3) via Riemann-Roch. We compare our volume formula with theirs and prove that our volume formula matches theirs in the case of triple reduced products of SU(3).

Department dc:contributor.department

Mathematics

Year dc:date.issued

2019

Author dc:creator

• Ji, Jia

Advisor dc:contributor.advisor

• Jeffrey, Lisa C

Handle dc:identifier.uri

http://hdl.handle.net/1807/97530

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/97530