EQUIVARIANT EXPONENTIALLY NASH VECTOR BUNDLES

A Note on Exponentially Nash G Manifolds and Vector Bundles

Quantization of Equivariant Vector Bundles

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry group.) In preparation for the main result, the quantization of coadjoint orbits is discussed in detail. This subject should not be confused with the quanti...

Construction of Equivariant Vector Bundles

Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...

Stably Trivial Equivariant Algebraic Vector Bundles

Let G be a reductive algebraic group over e, let F be a G-module, and let B be an affine G-variety, i.e., an affine variety with an algebraic action of G. Then B x F is in a natural way a G-vector bundle over B, which we denote by F. (All vector bundles here are algebraic.) A G-vector bundle over B is called trivial if it is isomorphic to F for some G-module F . From the endomorphism ring R of ...

Equivariant Vector Bundles on Quantum Homogeneous Spaces

The notion of quantum group equivariant homogeneous vector bundles on quantum homogeneous spaces is introduced. The category of such quantum vector bundles is shown to be exact, and its Grothendieck group is determined. It is also shown that the algebras of functions on quantum homogeneous spaces are noetherian.