3 papers
math.CA2025
Gelfand hypergeometric functions as solutions to the 2-dimensional Toda-Hirota equations II
Hironobu Kimura
We construct solutions of the -dimensional Toda-Hirota equation (2dTHE) expressed by the Gelfand hypergeometric function (Gelfand HGF) on the Grassmannian of…
math.CA2025
On the exterior power structure of the cohomology groups for the general hypergeometric integral
Hironobu Kimura
In this article we study the exterior power structure of the algebraic de Rham cohomology group associated with the Gelfand hypergeometric function and its confluent family. The hy…
math.CA2025
Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation
Hironobu Kimura
We construct solutions of the 2-dimensional Toda-Hirota equation (2dTHE) expressed by the solutions of the system of so-called Euler-Poisson-Darboux equations (EPD) in N complex va…