ABSTRACT
Studies of physical phenomena such as scattering amplitudes and quantum Hall effects in Grassmannian spaces have been attentively carried out in recent years. One of the main goals of this chapter is to present a clear and systematic review on these particular topics in mathematical physics. The chapter reviews some formal results of Aomoto’s generalized hypergeometric functions, based on Japanese textbooks. It presents a review in a pedagogical fashion since these results are not familiar enough to many physicists and mathematicians. As a simplest example, the chapter considers in detail Gauss' original hypergeometric functions in Aomoto's framework so as to familiarize ourselves to the concept of twisted homology and cohomology. It reviews the definition of Aomoto's generalized hypergeometric functions on Gr, interpreting their integral representations in terms of twisted homology and cohomology.
