5 research outputs found
Character and Multiplicity Formulas for Compact Hamiltonian G-spaces
Let K G be compact connected Lie groups with common maximal torus
T. Let (M, ) be a prequantisable compact connected symplectic manifold
with a Hamiltonian G-action. Geometric quantisation gives a virtual
representation of G; we give a formula for the character of this virtual
representation as a quotient of virtual characters of K. When M is a generic
coadjoint orbit our formula agrees with the Gross-Kostant-Ramond-Sternberg
formula. We then derive a generalisation of the Guillemin-Prato multiplicity
formula which, for a dominant integral weight of K, gives the
multiplicity in of the irreducible representation of K of highest weight
.Comment: 18 pages, 2 figures. To appear in Journal of Geometry and Physic