# Questions tagged [w-algebras]

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8
questions

**3**

votes

**1**answer

141 views

### Globalizing Feigin--Frenkel duality

Let $\mathfrak{g}$ be a semisimple Lie algebra, $\mathfrak{g}^L$ be its Langlands dual. Feigin--Frenkel duality says
$$
W^k(\mathfrak{g})=W^{k_L}(\mathfrak{g}^L)
$$
if $r'(k+h^{'})(k_L+h'_L)=1$, where ...

**3**

votes

**0**answers

207 views

### Center of affine W-algebras

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra and $k$ a complex number. Denote by $\hat{\mathfrak{g}}$ the corresponding affine Lie algebra ($\hat{\mathfrak{g}}=\mathfrak{g}((t)...

**8**

votes

**0**answers

458 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 ...

**5**

votes

**3**answers

378 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

**3**answers

416 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

**1**answer

374 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

**1**answer

658 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? ...

**9**

votes

**2**answers

680 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 ...