We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady’s privilege, is...

We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182 . AMS classification: 81T13, 81T75 The goal of this note is to consider gauge theories on noncommutative euclidean space and, in particular, to study the structure of gauge group. This group was an...

In this paper we prove the existence of the Dunkl weight function Kc,λ for any irreducible representation λ of any finite Coxeter group W , generalizing previous results of Dunkl. In particular, Kc,λ is a family of tempered distributions on the real reflection representation of W taking values in EndC(λ), with holomorphic dependence on the complex multi-parameter c. When the parameter c is real...

For each irreducible module of the symmetric group on N objects there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to certain Hermitian forms. These polynomials were studied by the author and J.-G. Luque using a Yang–Baxter graph te...

Let (G, K) be a Hermitian symmetric pair and let g and k denote the corresponding complexified Lie algebras. Let g = k⊕ p+⊕ p− be the usual decomposition of g as a k-module. K acts on the symmetric algebra S(p−). We determine the K-structure of all K-stable ideals of the algebra. Our results resemble the Pieri Rule for Young diagrams. The result implies a branching rule for a class of finite di...

In this paper the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category OS for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L “looks like” the cohomology with coefficients in a finite-dimensional module, as in Kostant’s theorem. A complete classification of these “Kostant modules”...

We consider a reductive dual pair (G,G′) in the stable range with G′ the smaller member and of Hermitian symmetric type. We study the theta lifting of nilpotent K ′ C-orbits, where K ′ is a maximal compact subgroup of G′ and we describe the precise KC-module structure of the regular function ring of the closure of the lifted nilpotent orbit of the symmetric pair (G,K). As an application, we pro...

In this paper the authors investigate infinite-dimensional representations L in blocks of the relative (parabolic) category OS for a complex simple Lie algebra, having the property that the cohomology of the nilradical with coefficients in L “looks like” the cohomology with coefficients in a finite-dimensional module, as in Kostant’s theorem. A complete classification of these “Kostant modules”...

[Formula: see text]-Poincaré invariant gauge theories on text]-Minkowski space-time, which are noncommutative analogs of the usual U(1) theory, exist only in five dimensions. These built from twisted connections a hermitian right module over algebra coding space-time. We show that twisting action this module, assumed to be copy it, affects neither value above dimension nor group defined as unit...