## 29 Citations

### Simplicity of vacuum modules and associated varieties

- Mathematics
- 2020

In this note, we prove that the universal affine vertex algebra associated with a simple Lie algebra $\mathfrak{g}$ is simple if and only if the associated variety of its unique simple quotient is…

### ON VERTEX ALGEBRAS AND ASSOCIATED VARIETIES

- Mathematics
- 2019

This note is an introduction to the notion of associated variety of a vertex algebra. It includes some basics on vertex algebras and Poisson vertex algebras. It is written in preparation to the…

### Associated varieties and Higgs branches (a survey)

- Mathematics
- 2017

Associated varieties of vertex algebras are analogue of the associated varieties of primitive ideals of the universal enveloping algebras of semisimple Lie algebras. They not only capture some of the…

### Quasi-lisse Vertex Algebras and Modular Linear Differential Equations

- Mathematics
- 2018

We introduce the notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex…

### Cohomological varieties associated to vertex operator algebras

- Mathematics
- 2022

. Given a vertex operator algebra V , one can attach a graded Poisson algebra called the C 2 -algebra R ( V ). The associate Poisson scheme provides an important invariant for V and has been studied…

### Some remarks on associated varieties of vertex operator superalgebras

- MathematicsEuropean Journal of Mathematics
- 2021

We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are "chiralizations" of their Zhu's Poisson…

### Vertex Algebras Associated with Hypertoric Varieties

- MathematicsInternational Mathematics Research Notices
- 2020

We construct a family of vertex algebras associated with a family of symplectic singularity/resolution, called hypertoric varieties. While the hypertoric varieties are constructed by a certain…

### Fe b 20 19 ARC SPACES AND CHIRAL SYMPLECTIC CORES

- Mathematics
- 2019

We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that any…

### REPRESENTATION THEORY OF W-ALGEBRAS AND HIGGS BRANCH CONJECTURE

- MathematicsProceedings of the International Congress of Mathematicians (ICM 2018)
- 2019

We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in…

## References

SHOWING 1-10 OF 75 REFERENCES

### A construction of some ideals in affine vertex algebras

- Mathematics
- 2001

We study ideals generated by singular vectors in vertex operator algebras associated with representations of affine Lie algebras of types A and C. We find new explicit formulas for singular vectors…

### Rationality of admissible affine vertex algebras in the category O

- Mathematics
- 2012

We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's…

### Integrable Highest Weight Modules over Affine Superalgebras and Appell's Function

- Mathematics
- 2001

Abstract:We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level 1 case. The analysis of this…

### Jet schemes and singularities

- Mathematics
- 2006

We give a self-contained presentation of the basic results on jet schemes of singular varieties. Applications are given to invariants of singularities, such as minimal log discrepancies. We simplify…

### Abelianizing Vertex Algebras

- Mathematics
- 2005

To every vertex algebra V we associate a canonical decreasing sequence of subspaces and prove that the associated graded vector space gr(V) is naturally a vertex Poisson algebra, in particular a…

### The index of centralizers of elements of reductive Lie algebras

- Mathematics
- 2009

For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer…

### SECTIONS OF SHEETS IN A REDUCTIVE ALGEBRAIC LIE ALGEBRA

- Mathematics
- 1983

It is shown that each sheet in a reductive algebraic Lie algebra possesses a geometric quotient. Bibliography: 3 titles.