2006-03-10
Alimjon Eshmatov, Cornell University
Lie group valued moment maps
This is an expository talk on q(uasi)-Hamiltonian G-spaces for which
the moment map takes values in the group G itself rather than in the
dual of Lie algebra. This theory was developed in the celebrated work
of Alekseev-Malkin-Meinrenken[1998]. Their main motivation for
introducing group valued moment maps was to study the moduli space of
flat connections on closed 2-manifolds.
In this talk we will give the definition of q-Hamiltonian G-spaces and
mention some examples. We will also discuss how they are related to
usual Hamiltonian spaces (linearization and exponentiation). If time
permits we will talk about a natural bijective correspondence between
infinite-dimensional Hamiltonian LG-spaces (Loop-group spaces) and
q-Hamiltonian G-spaces.