Related papers: $K$-theoretic Hall algebras and Coulomb branches

We develop a new method for constructing $3d$ $\mathcal{N}=4$ Coulomb branch chiral rings in terms of gauge-invariant generators and relations while making the global symmetry manifest. Our examples generalise to all balanced quivers of…

I give a simple construction of certain Coulomb branches $C_{3,4}(G;E)$ of gauge theory in 3 and 4 dimensions defined by Nakajima et al. for a compact Lie group $G$ and a polarisable quaternionic representation $E$. The manifolds $C(G; 0)$…

We compare the integral category O of shifted affine quantum groups of symmetric and non symmetric types. To do so we compute the K-theoretic analog of the Coulomb branches with symmetrizers introduced by Nakajima and Weekes. This yields an…

In this paper we give a geometric construction of the quantum group Ut(G) using Nakajima categories, which were developed in [29]. Our methods allow us to establish a direct connection between the algebraic realization of the quantum group…

We study Seiberg duality of quiver gauge theories associated to the complex cone over the second del Pezzo surface. Homomorphisms in the path algebra of the quivers in each of these cases satisfy relations which follow from a superpotential…

In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…

We study the Coulomb-branch sector of 3D $\mathcal{N}=4$ gauge theories with half-hypermultiplets in general pseudoreal representations $\mathbf{R}$ ("noncotangent" theories). This yields (short) quantization of the Coulomb branch and…

We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a ``$q=0$'' version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of…

For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a…

We propose a construction of the quantum-corrected Coulomb branch of a general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the…

We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman, which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of…

This paper classifies all Higgs branch Higgsing patterns for simply-laced unitary quiver gauge theories with eight supercharges (including multiple loops) and introduces a Higgs branch subtraction algorithm. All possible minimal transitions…

We compute the convolution product on the equivariant K-groups of the cyclic quiver variety. We get a q-analogue of double-loop algebras, closely related to the toroidal quantum groups previously studied by the authors. We also give a…

Recently the authors initiated an $\imath$Hall algebra approach to (universal) $\imath$quantum groups arising from quantum symmetric pairs. In this paper we construct and study BGP type reflection functors which lead to isomorphisms of the…

We provide a generators and relation description of the deformed W_{1+\infty}-algebra introduced in previous joint work of E. Vasserot and the second author. This gives a presentation of the (spherical) cohomological Hall algebra of the…

We construct an equivalence of graded Abelian categories from a category of representations of the quiver-Hecke algebra of type $A_1^{(1)}$ to the category of equivariant perverse coherent sheaves on the nilpotent cone of type $A$. We prove…

We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster…

We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra $\mathfrak g$. We analyse classes of quiver theories, with Classical gauge and flavour…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

We present a new family of IR dualities in three space-time dimensions with eight supercharges. In contrast to 3d mirror symmetry, these dualities map Coulomb branches to Coulomb branches and Higgs branches to Higgs branches in the deep IR.…