Alexey Sevastyanov (Aberdeen):
q-W algebras, Mickelsson algebras and Zhelobenko operators
q-W algebras were introduced in the mid 90-th as analogues of W-algebras in a conjectural q-version of the geometric Langlands correspondence and as hypothetic symmetry algebras for massive two-dimensional field theories.
In this talk I shall consider finitely generated versions of q-W algebras. I will show that q-W algebras belong to the class of the so-called Mickelsson algebras. They can be described in terms of certain analogues of Zhelobenko operators.