Szegö Kernels Associated with Zuckerman Modules

Theta Functions and Szegö Kernels

We study relations between two fundamental constructions associated to vector bundles on a smooth complex projective curve: the theta function (a section of a line bundle on the moduli space of vector bundles) and the Szegö kernel (a section of a vector bundle on the square of the curve). Two types of relations are demonstrated. First, we establish a higher–rank version of the prime form, descr...

Szegö Kernels for Certain Unbounded Domains

Moment Maps and Equivariant Szegö Kernels

Let M be a connected n-dimensional complex projective manifold and consider an Hermitian ample holomorphic line bundle (L, hL) on M . Suppose that the unique compatible covariant derivative ∇L on L has curvature −2πiΩ, where Ω is a Kähler form. Let G be a compact connected semisimple Lie group and μ : G×M → M a holomorphic Hamiltonian action on (M,Ω). Let g be the Lie algebra of G, and denote b...

Fekete-Szegö Problem of Functions Associated with Hyperbolic Domains

In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, Fekete-Szegö inequality is one of such vastly studied a...

Szegö Kernels, Toeplitz Operators, and Equivariant Fixed Point Formulae

The aim of this paper is to apply algebro-geometric Szegö kernels to the asymptotic study of a class of trace formulae in equivariant geometric quantization and algebraic geometry. Let (M,J) be a connected complex projective manifold, of complex dimension d, and let A be an ample line bundle on it. Let, in addition, G be a compact and connected g-dimensional Lie group acting holomorphically on ...