"Introduction to the Theory of Representations of Quantum Groups"
The aim of this course is to study from scratch some basic and explicit examples of representations of various quantum groups, and to relate them to active and fast developing fiels of research. First, we will focus on simple representations of quantum algebras of type sl(2), and relate them to the colored Jones polynomials of knots and the volume conjecture. Besides we will construct the Kirillov-Reshetikhin modules of sl(2) quantum affine algebras, describe the T-system exact sequence explicitely and relate it to fermionic formulas and the corresponding integrable systems.