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There are theories of classical, basic and elliptic hypergeometric series; rational, trigonometric and elliptic Dunkl operators; classical, (small) quantum and elliptic cohomology and K-theory of flag varieties (classical and quantum Schubert and Grothendieck Calculi). I will try to explain that all the theories mentioned above correspond to different representations of a certain "universal" noncommutative quadratic algebra. The main goal of my talk will be to draw attention to that quadratic algebra and to describe some of its algebraic and combinatorial properties. The main part of my talk will be elementary and should be accessible to a wide audience. After the seminar we will take the speaker to lunch. See the Algebra Seminar web page for information about other seminars in the series. Anthony Henderson anthonyh@maths.usyd.edu.au. |