# Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras

@inproceedings{Arakawa2021SingularitiesON, title={Singularities of nilpotent Slodowy slices and collapsing levels of W-algebras}, author={Tomoyuki Arakawa and Jethro van Ekeren and Anne Moreau}, year={2021} }

We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex algebras and their finite extensions at specific admissible levels. In particular we identify many new collapsing levels for W-algebras.

## 8 Citations

### Reduction by stages for finite W-algebras

- Mathematics
- 2022

. Let g be a semisimple Lie algebra: its dual space g ∗ is a Poisson variety. It is well known that for each nilpotent element f in g , it is possible to construct a new Poisson structure by…

### OPEs of rank two W-algebras

- Mathematics
- 2022

. In this short note, we provide OPEs for several aﬃne W -algebras associated with Lie algebras of rank two and give some direct applications.

### Cosets from equivariant W-algebras

- Mathematics
- 2022

. The equivariant W -algebra of a simple Lie algebra g is a BRST reduction of the algebra of chiral diﬀerential operators on the Lie group of g . We construct a family of vertex algebras A [ g ,κ,n ]…

### Category $\mathcal O$ for vertex algebras of $\mathfrak{osp}_{1|2n}$

- Mathematics
- 2022

We show that the affine vertex superalgebra V k(osp1|2n) at generic level k embeds in the equivariant W-algebra of sp2n times 4n free fermions. This has two corollaries: (1) it provides a new proof…

### On the nilpotent orbits arising from admissible affine vertex algebras

- MathematicsProceedings of the London Mathematical Society
- 2022

We give a simple description of the closure of the nilpotent orbits appearing as associated varieties of admissible affine vertex algebras in terms of primitive ideals.

### On the representation theory of the vertex algebra L−5/2(sl(4))

- MathematicsCommunications in Contemporary Mathematics
- 2021

We study the representation theory of non-admissible simple affine vertex algebra [Formula: see text]. We determine an explicit formula for the singular vector of conformal weight four in the…

### W algebras, cosets and VOAs for 4d $$ \mathcal{N} $$ = 2 SCFTs from M5 branes

- Mathematics
- 2021

We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with…

### Schur sector of Argyres-Douglas theory and $W$-algebra

- Mathematics
- 2019

We study the Schur index, the Zhu's $C_2$ algebra, and the Macdonald index of a four dimensional $\mathcal{N}=2$ Argyres-Douglas (AD) theories from the structure of the associated two dimensional…