The object of this paper is the relation between the Szegö kernel of an ample line bundle on a complex projective manifold, M , and the Szegö kernel of the induced polarization on the quotient of M by the holomorphic action of a compact Lie group, G. Let M be an n-dimensional complex projective manifold and L an ample line bundle on it. Suppose a connected compact Lie group G acts on M as a gro...

We classify those manifolds mentioned in the title which have nite topological type. Namely we show that any such connected M 4n is isomorphic to a hyperkk ahler quotient of a at quaternionic vector space H d by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n ? 1 whose isometry group has rank n + 1 is isometric to a 3-Sasakian quo...

Let W be a Coxeter group with Coxeter graph Γ. Let H be theassociated Hecke algebra. We define a certain ideal I in H and study thequotient algebra H̄ = H/I. We show that when Γ is one of the infinite seriesof graphs of type E, the quotient is semi-simple. We examine the cell structuresof these algebras and construct their irreducible representations. We discussthe case where...

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohom...

a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...

Gromov constructed uncountably many pairwise non-isomorphic discrete groups with Kazhdan's property (T). We will show that no separable II 1-factor can contain all these groups in its unitary group. In particular, no separable II 1-factor can contain all separable II 1-factors in it. We also show that the full group C *-algebras of some of these groups fail the lifting property. We recall that ...

the largest class of algebraic hyper structures satisfying the module like axioms is the v h -module. in this paper, we consider the category of v h -modules and prove that the direct limit alwaysexists in this category. direct limits are defined by a universal property, and so are unique. the mostpowerful tool in order to obtain a module from a given v h - module is the quotient out procedure....