Abstract:
Double affine Hecke algebras (DAHAs) were introduced by Cherednik to study Knizhnik-Zamolodchikov equations in the late 80s and became popular as Cherednik himself was able to use their theory to proveMacdonald’s constant term conjecture in 1995. Since then, the theory of DAHAs has been connected to several areas of Mathematics, such as Geometry, Knot Theory, Quantum Algebra and Combinatorics.
We will start by constructing the DAHA of type $GL_n$ step by step by gluing two copies of the affine Hecke algebra. We will then see how to construct representations of the DAHA at rootsof unity in a purely combinatorial fashion by using certain tableaux. In the final part of the talk, we will connect these representations to the theory of quantum groups.
BBB at the following link: PhD Colloquia – VSM (vsmath.at)