ACORT

The proposal aims to study and solve recent problems in representation theory by using algebraic and combinatorial technics. It gathers young researchers in France working in different and complementary aspects of the areas. The subjects we plan to study are quite large and decompose as follows: the representation theory of braid groups, complex reflection groups and their deformations, the Kazhdan-Lusztig theory and generalization, the representation theory of quantum groups. These notions are at the heart of an intense research activity in most of the main mathematical countries over the world. They also have numerous fruitful interactions which are far to be completely elucidated. We plan to organize each of the four years of the project a general meeting gathering in particular all the members and summarizing the advances obtained or the new questions encountered. Additional working sessions, with introduction courses devoted to one of the previous themes will also be organized during the two first years of the project suited both for Ph. D. students and members of our team. In addition, we plan to organize two-days workshops every year on Algebraic Combinatorics (such workshops have already been organized in Tours or Besançon). As usual, we will need some funds for mobility of participants to the program (in order to organize research groups on each task of the project), invitations of foreigner colleagues and documentation.