A Star Product for Complex Grassmann Manifolds
نویسنده
چکیده
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 Gp,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 Gp,q(C) onto which this projection acts as an algebra-epimorphism. ∗e-mail: [email protected]
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