There is a well-established procedure for quantizing the Drinfeld-Sokolov reduction for an affine Lie algebra. In particular, this paper of de Boer and Tjin describes an algorithm to produce the ...
Is there a paper in which are all the irreps of the finite W-algebra with trivial action of the center are classified, in the case of $\mathfrak sl_3(\mathbb C)$ and the minimal orbit?
Does anybody know if there is an analog of the Cartan (anti)involution for W-algebra associated to a nilpotent element e, which is principal in some Levi subalgebra of semi-simple Lie algebra g? ...
My question is prompted by Ben Webster's answer to this question. Is there a notion of tensor product for representations of a finite W-algebra? I thought about this question years ago in the ...