4
votes
3answers
299 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 ...
3
votes
1answer
327 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 ...
12
votes
1answer
576 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? ...