On “a small” GRAND UNIFICATION

There are surprising similarities in the algebraic properties of Classical, Basic and Elliptic Hypergeometric functions, as well as in the study of Rational, Hypergeometric and Elliptic Calogero–Moser models, as well as in the description of classical and quantum cohomology and K-theory rings of the flag varieties of type A.
The main goal of my talk is to present a modest explanation of such similarities.
To do that, I introduce a certain quadratic algebra together with a distinguish set of mutually commuting elements inside it (the so-called Dunkl elements), in such a way that the items mentioned in the beginning of my Abstract, correspond to different representations of the quadratic algebra in question. Some applications to the Classical and Quantum Schubert and Grothendieck Calculi will be stated.