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12
votes
1answer
587 views

Cartan involution for finite W-algebras

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? ...
8
votes
2answers
527 views

Is the category of representations of a finite W-algebra monoidal?

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 ...
5
votes
3answers
316 views

Good even grading and principal Levi type

Let $\mathfrak g$ be a simple Lie algebra over $\mathbb C$ and let $e$ be a nilpotent element in it. In the theory of finite W-algebras one often encounters the following two conditions: 1) $e$ is ...
4
votes
0answers
157 views

Quantum Drinfeld-Sokolov reduction for a module

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 ...
3
votes
3answers
365 views

Irreducible representations of W-algebra in case $\mathfrak sl_3$

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?
3
votes
1answer
336 views

A question on the construction of finite W-algebras

In a well known construction of finite W-algebras, one first constructs a certain nilpotent subalgebra $\mathfrak{m}$ along with a character $\chi:\mathfrak{m}\rightarrow \mathbb{C}$. Then one defines ...