On hypergeometric functions and function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On Hypergeometric Functions Connected with Quantum Cohomology of Flag Spaces

In the Givental’s work on the Gromov-Witten invariants for projective complete intersections, [G1], the principal role is played by certain formal power series connected with the quantum cohomology of a manifold. One has a manifold X with a natural torus action, with the finite number of fixed points, and one has a power series Zw associated with each fixed point xw. The coefficients of these s...

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

Three Lectures on Hypergeometric Functions

In this course we will study multivariate hypergeometric functions in the sense of Gel’fand, Kapranov, and Zelevinsky (GKZ systems). These functions generalize the classical hypergeometric functions of Gauss, Horn, Appell, and Lauricella. We will emphasize the algebraic methods of Saito, Sturmfels, and Takayama to construct hypergeometric series and the connection with deformation techniques in...

Notes on A-hypergeometric Functions