We study finite-dimensional representations of current algebras, loop algebras and their
quantized versions. For the current algebra of a simple Lie algebra of type ADE, we show …

We show that every Weyl module for a current algebra has a filtration whose successive
quotients are isomorphic to Demazure modules, and that the path model for a tensor product …

In this paper, we introduce a family of indecomposable finite-dimensional graded modules
for the current algebra associated to a simple Lie algebra. These modules are indexed by …

We define cylindric versions of skew Macdonald functions P λ/μ (q, t) for the special cases q=
0 or t= 0. Fixing two integers n> 2 and k> 0 we shift the skew diagram λ/μ, viewed as a …

We construct an injection from the set of r-fans of Dyck paths (resp. vacillating tableaux) of
length n into the set of chord diagrams on [n] that intertwines promotion and rotation. This is …

In this paper, we give a direct proof of the equality of certain generatingfunction associated
with tensor product multiplicities of Kirillov-Reshetikhin modules of the untwisted Yangian for …

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 …

We study the category of finite-dimensional bigraded representations of toroidal current
algebras associated to finite-dimensional complex simple Lie algebras. Using the theory of …

A perfect crystal of any level is constructed for the Kirillov–Reshetikhin module of Uq (D4 (3))
corresponding to the middle vertex of the Dynkin diagram. The actions of Kashiwara …