Related papers: Feigin-Semikhatov conjecture and related topics

Recently, motivated by supersymmetric gauge theory, Cachazo, Douglas, Seiberg, and Witten proposed a conjecture about finite dimensional simple Lie algebras, and checked it in the classical cases. We prove the conjecture for type G_2, and…

We study the representation theory of the Kazama-Suzuki coset vertex operator superalgebra associated with the pair of a complex simple Lie algebra and its Cartan subalgebra. In the case of type $A_{1}$, B.L. Feigin, A.M. Semikhatov, and…

We review some basic features of the Lie-algebraic classification of W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out the role of affine Lie algebras. We emphasize that the supersymmetric extensions of the above…

This paper consists of two parts. In the first part, we prove that when $\mathfrak{g}$ is a simple basic Lie superalgebra with a principal odd nilpotent element $f$, the W-algebra $W^k(\mathfrak{g}, F)$ for $F=-\frac{1}{2}[f,f]$ is…

We study the affine analogue $\mathrm{FT}_p(\mathfrak{sl}_2)$ of the triplet algebra. We show that $\mathrm{FT}_p(\mathfrak{sl}_2)$ is quasi-lisse and the associated variety is the nilpotent cone of $\mathfrak{sl}_2$. We realize…

The invariant subalgebra H^+ of the Heisenberg vertex algebra H under its automorphism group Z/2Z was shown by Dong-Nagatomo to be a W-algebra of type W(2,4). Similarly, the rank n Heisenberg vertex algebra H(n) has the orthogonal group…

We establish rigid tensor category structure on finitely-generated weight modules for the subregular $W$-algebras of $\mathfrak{sl}_n$ at levels $ - n + \frac{n}{n+1}$ (the $\mathcal{B}_{n+1}$-algebras of Creutzig-Ridout-Wood) and at levels…

In this paper we prove a general result saying that under certain hypothesis an embedding of an affine vertex algebra into an affine $W$--algebra is conformal if and only if their central charges coincide. This result extends our previous…

Let $\mathfrak{g}$ be a finite-dimensional semisimple complex Lie algebra and $\theta$ an involutive automorphism of $\mathfrak{g}$. According to G. Letzter, S. Kolb and M. Balagovi\'c the fixed-point subalgebra $\mathfrak{k} =…

$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…

First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…

For each simple Lie algebra g consider the corresponding affine vertex algebra V_{crit}(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem…

This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras…

We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…

In this note, given a pair $(\mathfrak{g}, \lambda)$, where $\mathfrak{g}$ is a complex semisimple Lie algebra and $\lambda \in \mathfrak{h}^*$ is a dominant integral weight of $\mathfrak{g}$, where $\mathfrak{h} \subset \mathfrak{g}$ is…

We introduce a notion of $Q$-algebra that can be considered as a generalization of the notion of $Q$-manifold (a supermanifold equipped with an odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on modules over…

We introduce the notion of a conformal pseudo-subriemannian fundamental graded Lie algebra of semisimple type. Moreover we give a classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their…

By using the coproduct and evaluation map for the affine Yangian and the Miura map for non-rectangular $W$-algebras, we construct a homomorphism from the affine Yangian associated with $\widehat{\mathfrak{sl}}(n)$ to the universal…

For any simple Lie algebra $\mathfrak{g}$ and an element $\mu\in\mathfrak{g}^*$, the corresponding commutative subalgebra $\mathcal{A}_{\mu}$ of $\mathcal{U}(\mathfrak{g})$ is defined as a homomorphic image of the Feigin-Frenkel centre…

By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…