Abstract
We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on
C
(p+q)⋅p ∗
, the space of
(p+q)×p
matrices of rank p, invariant under the right action of
Gl(p,C)
can be regarded as functions on the Grassmann manifold
G
p,q
(C)
, but do not form a subalgebra whereas functions only invariant under the unitary subgroup
U(p)⊂Gl(p,C)
do. The idea is to construct a projection from
U(p)
- onto
Gl(p,C)
-invariant functions, whose kernel is an ideal. This projection can be used to define a star-algebra on
G
p,q
(C)
onto which this projection acts as an algebra-epimorphism.