Heckman, Kostant, and Steinberg formulas for symplectic manifolds

✍ Scribed by Victor Guillemin; Elisa Prato

• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 832 KB
• Volume: 82
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(90)90087-4

✦ Synopsis

Let M be a compact symplectic manifold on which a compact connected Lie group, K, acts in a Hamiltonian fashion. In Part I we deriye a formula for J*( ljh, l which generalizes the Heckman formula for' co-adjoint orbits.

(Here J is the moment map associated with the action of K on M and /1,,, the Liouville measure on M.) In Part II we derive a "quantum" analogue of this formula which extends to the symplectic setting classical multiplicity formulas of Kostant and Steinberg.