Brane systems provide a large class of gauge theories that arise in string theory. This paper
demonstrates how such brane systems fit with a somewhat exotic geometric object, called …

We develop the representation theory of shifted quantum affine algebras and of their
truncations, which appeared in the study of quantized K-theoretic Coulomb branches of 3d …

We define an integral form of shifted quantum affine algebras of type A and construct
Poincaré–Birkhoff–Witt–Drinfeld bases for them. When the shift is trivial, our integral form …

Given a representation N of a reductive group G, Braverman–Finkelberg–Nakajima have
defined a remarkable Poisson variety called the Coulomb branch. Their construction of this …

Symplectic resolutions are an exciting new frontier of research in representation theory. One
of the most fascinating aspects of this study is symplectic duality: the observation that these …

We study the Coulomb branches of $3 d $$\mathcal {N}= 4$ quiver gauge theories, focusing
on the generators for their quantized coordinate rings. We show that there is a surjective …

The Hikita conjecture relates the coordinate ring of a conical symplectic singularity to the
cohomology ring of a symplectic resolution of the dual conical symplectic singularity. We …

We develop a theory of parabolic induction and restriction functors relating modules over
Coulomb branch algebras, in the sense of Braverman-Finkelberg-Nakajima. Our functors …

In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential
operators. The structure of these modules is described with the aid of the Postnikov-Stanley …

We continue our study of noncommutative resolutions of Coulomb branches in the case of
quiver gauge theories. These include the Slodowy slices in type A and symmetric powers in …