This is a companion paper of arXiv: 1601.03586. We study Coulomb branches of unframed
and framed quiver gauge theories of type $ ADE $. In the unframed case they are …

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 construct a Poincaré–Birkhoff–Witt type basis for the Weyl modules [V. Chari, A.
Pressley, Weyl modules for classical and quantum affine algebras, Represent. Theory 5 …

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 …

We prove the (generalized) coherence conjecture proposed by Pappas and Rapoport. As a
corollary, one of their theorems, which describes the geometry of the special fibers of the …

We lift the parabolic quantum Bruhat graph (QBG) into the Bruhat order on the affine Weyl
group and into Littelmann's poset on level-zero weights. We establish a quantum analog of …

We establish the equality of the specialization of the Macdonald polynomial at with the
graded character of a tensor product of “single-column” Kirillov–Reshetikhin modules for …

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 a family of graded restricted modules for the polynomial current algebra
associated to a simple Lie algebra. We study the graded character of these modules and …

Truncated shifted Yangians are a family of algebras which are natural quantizations of slices
in the affine Grassmannian. We study the highest weight representations of these algebras …