Inspired by a number of recent papers by Corteel, Dousse, Foda, Uncu and Welsh on
cylindric partitions and Rogers–Ramanujan-type identities, we obtain the $\mathrm {A} _2 …

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced,
as a generalization of the notion of principal subspaces. Bases and the graded dimensions …

In this note we prove linear independence of the combinatorial spanning set for standard C ℓ
(1)-module L (k Λ 0) by establishing a connection with the combinatorial basis of Feigin …

We use vertex operator algebras and intertwining operators to study certain substructures of
standard-modules, allowing us to conceptually obtain the classical Rogers–Ramanujan …

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 “chiral-quantizations" of …

We give a commutative algebra viewpoint on Andrews recursive formula for the partitions
appearing in Gordon's identities, which are a generalization of Rogers–Ramanujan …

We introduce what we call the principal subalgebra of a lattice vertex (super) algebra
associated to an arbitrary Z-basis of the lattice. In the first part (to appear), the second author …

Generalizing some of our earlier work, we prove natural presentations of the principal
subspaces of the level one standard modules for the untwisted affine Lie algebras of types …

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin–
Stoyanovsky's principal subspaces associated to standard modules for both untwisted and …

We give an a priori proof of the known presentations of (that is, completeness of families of
relations for) the principal subspaces of all the standard A1 (1)-modules. These …