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 …

The Schur index of the (A_1, X_n)(A 1, X n)-Argyres–Douglas theory is conjecturally a
character of a vertex operator algebra. Here such vertex algebras are found for the A_ odd A …

These are lecture notes from author's mini-course on W-algebras during Session 1:“Vertex
algebras, W-algebras, and application” of INdAM Intensive research period “Perspectives in …

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 …

ABSTRACT Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a
homomorphism from the affine super Yangian Yε1, ε2 (̂sl (m∣ n)) to the universal …

We define higher quantum Airy structures as generalizations of the Kontsevich–Soibelman
quantum Airy structures by allowing differential operators of arbitrary order (instead of only …

We construct algebra homomorphisms from affine Yangians to the current algebras of
rectangular W-algebras both in type A. The construction is given via the coproduct and the …

A bstract We construct a quadratic basis of generators of matrix-extended\({\mathcal {W}} _
{1+\infty}\) using a generalization of the Miura transformation. This makes it possible to …

A bstract We analyze the asymptotic symmetry of higher spin gravity with M× M matrix valued
fields, which is given by rectangular W-algebras with su (M) symmetry. The matrix valued …

We prove the conjectural isomorphism between the level $ k $$\widehat {\mathfrak {sl}} _2 $-
parafermion vertex operator algebra and the $(k+ 1, k+ 2) $-minimal series $ W_k $-algebra …