We propose a construction for the quantum-corrected Coulomb branch of a general 3d
gauge theory with N= 4 N= 4 supersymmetry, in terms of local coordinates associated with …

A bstract We introduce several families of\(\mathcal {N}=\left (2,\2\right)\) UV boundary
conditions in 3d\(\mathcal {N}= 4\) gaugetheoriesandstudytheirIRimagesinsigma …

We define and study category $\mathcal O $ for a symplectic resolution, generalizing the
classical BGG category $\mathcal O $, which is associated with the Springer resolution. This …

The dazzling success of algebraic geometry... has so much reorientated the field that one
particular protagonist has suggested, no doubt with much justification, that enveloping …

We calculate the category of $ D $-modules on the loop space of the affine line in coherent
terms. Specifically, we find that this category is derived equivalent to the category of ind …

We re-examine some topics in representation theory of Lie algebras and Springer theory in
a more general context, viewing the universal enveloping algebra as an example of the …

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 …

We study equivalences for category Op of the rational Cherednik algebras Hp of type Gl
(n)=(µl) n Sn: a highest weight equivalence between Op and Oσ (p) for σ∈ Sl and an action …

We consider homological mirror symmetry in the context of hypertoric varieties, showing that
an appropriate category of B–branes (that is, coherent sheaves) on an additive hypertoric …

This paper develops a general theory of canonical bases and how they arise naturally in the
context of categorification. As an application, we show that Lusztig's canonical basis in the …