RESEARCH IN PAIRS

Reduction algebras and quantum groups
October 10 – 21, 2016
   Mickelsson algebras (or reduction algebras) were introduced for the study of Harish-Chandra modules of reductive groups. The Mickelsson algebra, related to a real reductive group G, acts on the space of highest weight vectors of its maximal compact subgroup, and each irreducible Harish-Chandra module of the initial reductive group is uniquely characterized by this action. The reduction algebra can be realized as a sub-quotient of the universal enveloping algebra of the Lie algebra of G. A similar construction can be given for any associative algebra A, which contains a universal enveloping algebra (or its q-analog) of a contragredient Lie algebra g.
   One of our goals is to establish a close connection between Mickelsson algebras and quantum groups. This includes: from one side a Yang-Baxter type description of various reduction algebras and the use of quantum group techniques for their algebraic description; from another side the application of the methods developed in our investigations of Mickelsson algebras to dynamical quantum groups and related integrable models. Another goal is a study of the representation theory of Mickelsson algebras with applications to classical problems in the theory of Lie groups and in mathematical physics.


Participants

Sergey Khoroshkin (HSE Moscow)
Oleg 
Ogievetsky (Aix-Marseille Université)

Sponsor