We prove the long-standing conjecture on the coset construction of the minimal series
principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's …

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 …

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

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 …

Let gg be a simple finite-dimensional Lie superalgebra with a non-degenerate
supersymmetric even invariant bilinear form, fa nilpotent element in the even part of gg, Γ Γ a …

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 For any 4d\(\mathcal {N}\)= 2 SCFT, there is a subsector described by a 2d chiral
algebra. The vacuum character of the chiral algebra reproduces the Schur index of the …

We introduce geometric quantization in the setting of shifted symplectic structures. We define
Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric …

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 …