# Cosets of the $\mathcal{W}^k(\mathfrak{sl}_4, f_{\text{subreg}})$-algebra

@article{Creutzig2017CosetsOT, title={Cosets of the \$\mathcal\{W\}^k(\mathfrak\{sl\}\_4, f\_\{\text\{subreg\}\})\$-algebra}, author={Thomas Creutzig and Andrew R. Linshaw}, journal={arXiv: Representation Theory}, year={2017} }

Let $\mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}})$ be the universal $\mathcal{W}$-algebra associated to $\mathfrak{sl}_4$ with its subregular nilpotent element, and let $\mathcal {W}_k(\mathfrak{sl}_4, f_{\text {subreg}})$ be its simple quotient. There is a Heisenberg subalgebra $\mathcal{H}$, and we denote by $\mathcal{C}^k$ the coset $\text{Com}(\mathcal{H}, \mathcal {W}^k(\mathfrak{sl}_4, f_{\text {subreg}}))$, and by $\mathcal{C}_k$ its simple quotient. We show that for $k=-4+(m+4)/3… Expand

#### 7 Citations

Universal two-parameter $\mathcal{W}_{\infty}$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots, N)$

- Mathematics, Physics
- 2017

We prove the longstanding physics conjecture that there exists a unique two-parameter $\mathcal{W}_{\infty}$-algebra which is freely generated of type $\mathcal{W}(2,3,\dots)$, and generated by the… Expand

Universal two-parameter even spin W∞-algebra

- Mathematics, Physics
- Advances in Mathematics
- 2019

Abstract We construct the unique two-parameter vertex algebra which is freely generated of type W ( 2 , 4 , 6 , … ) , and generated by the weights 2 and 4 fields. Subject to some mild constraints,… Expand

SCHUR–WEYL DUALITY FOR HEISENBERG COSETS

- Mathematics, Physics
- 2016

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H and let C = Com(H;V) be the coset of H in V. Assuming that the module categories of interest are vertex… Expand

Simple current extensions beyond semi-simplicity

- Mathematics
- Communications in Contemporary Mathematics
- 2019

Let [Formula: see text] be a simple vertex operator algebra (VOA) and consider a representation category of [Formula: see text] that is a vertex tensor category in the sense of Huang–Lepowsky. In… Expand

Fusion categories for affine vertex algebras at admissible levels

- Mathematics
- Selecta Mathematica
- 2019

The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the… Expand

Simple Current Extensions of Tensor Products of Vertex Operator Algebras

- Mathematics
- 2018

We study simple current extensions of tensor products of two vertex operator algebras satisfying certain conditions. We establish the relationship between the fusion rule for the simple current… Expand

Duality of subregular W-algebras and principal W-superalgebras

- Mathematics, Physics
- 2020

We prove Feigin-Frenkel type dualities between subregular W-algebras of type A, B and principal W-superalgebras of type $\mathfrak{sl}(1|n), \mathfrak{osp}(2|2n)$. The type A case proves a conjecture… Expand

#### References

SHOWING 1-10 OF 61 REFERENCES

Cosets of Bershadsky–Polyakov algebras and rational $${\mathcal W}$$W-algebras of type A

- Mathematics
- 2015

The Bershadsky–Polyakov algebra is the $${\mathcal W}$$W-algebra associated to $${\mathfrak s}{\mathfrak l}_3$$sl3 with its minimal nilpotent element $$f_{\theta }$$fθ. For notational convenience we… Expand

Orbifolds and Cosets of Minimal $${\mathcal{W}}$$W-Algebras

- Mathematics, Physics
- 2017

Let $${\mathfrak{g}}$$g be a simple, finite-dimensional Lie (super)algebra equipped with an embedding of $${\mathfrak{s}\mathfrak{l}_2}$$sl2 inducing the minimal gradation on $${\mathfrak{g}}$$g. The… Expand

The Structure of the Kac–Wang–Yan Algebra

- Mathematics, Physics
- 2016

The Lie algebra $${\mathcal{D}}$$D of regular differential operators on the circle has a universal central extension $${\hat{\mathcal{D}}}$$D^. The invariant subalgebra $${\hat{\mathcal{D}}^+}$$D^+… Expand

A Hilbert theorem for vertex algebras

- Mathematics
- 2009

Given a simple vertex algebra $$ \mathcal{A} $$ and a reductive group G of automorphisms of $$ \mathcal{A} $$, the invariant subalgebra $$ {\mathcal{A}^G} $$ is strongly finitely generated in most… Expand

W-algebras for Argyres–Douglas theories

- Physics, Mathematics
- 2017

The Schur index of the $$(A_1, X_n)$$(A1,Xn)-Argyres–Douglas theory is conjecturally a character of a vertex operator algebra. Here such vertex algebras are found for the $$A_{\text {odd}}$$Aodd and… Expand

Invariant theory and the $\mathcal{W}_{1+\infty}$ algebra with negative integral central charge

- Mathematics
- 2011

The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer… Expand

Coset Constructions of Logarithmic (1, p) Models

- Mathematics, Physics
- 2013

One of the best understood families of logarithmic onformal field theories consists of the (1, p) models (p = 2, 3, . . .) of central charge c1, p=1 − 6(p − 1)2/p. This family includes the theories… Expand

Vertex Algebras for S-duality

- Physics, Mathematics
- 2017

We define new deformable families of vertex operator algebras $\mathfrak{A}[\mathfrak{g}, \Psi, \sigma]$ associated to a large set of S-duality operations in four-dimensional supersymmetric gauge… Expand

Tensor categories for vertex operator superalgebra extensions

- Mathematics, Physics
- 2017

Let $V$ be a vertex operator algebra with a category $\mathcal{C}$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, and let $A$ be a… Expand

$ \mathcal{N}=1 $ supersymmetric higher spin holography on AdS3

- Physics
- 2012

A bstractWe propose a duality between a higher spin $ \mathcal{N}=1 $ supergravity on AdS3 and a large N limit of a family of $ \mathcal{N}=\left( {1,1} \right) $ superconformal field theories. The… Expand