Vertex operator algebra theory is a new area of mathematics. It has been an exciting and
ever-growing subject from the beginning, starting even before R. Borcherds introduced the …

In this volume, the authors show that a set of local admissible fields generates a vertex
algebra. For an affine Lie algebra $\tilde {\frak g} $, they construct the corresponding level …

We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to
some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a …

This is the first of a series of papers studying combinatorial (with no “subtractions”) bases
and characters of standard modules for affine Lie algebras, as well as various subspaces …

We introduce a technique to construct Andrews–Gordon type evidently positive series as
generating functions for the partitions satisfying various gap conditions. The construction …

We give manifestly positive Andrews-Gordon type series for the level 3 standard modules of
the affine Lie algebra of type $ A^{(1)} _2 $. We also give corresponding bipartition identities …

We give a new simple formula for the energy function of a level $1 $ perfect crystal of type $
C_n^{(1)} $ introduced by Kang, Kashiwara and Misra. We use this to give several …

Kanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some
of which are related to level 2 characters of the affine Lie algebra A_9^(2) A 9 (2). Many of …

We use an integral method to establish a number of Rogers-Ramanujan type identities
involving double and triple sums. The key step for proving such identities is to find some …

Abstract We construct Andrews–Gordon type positive series as generating functions of
partitions satisfying certain difference conditions in six conjectures by Kanade and Russell …