Related papers: Nonabelian shift operators and shifted Yangians

In \cite{GS1} the notion of braided Yangians of Reflection Equation type was introduced. Each of these algebras is associated with an involutive or Hecke symmetry $R$. Besides, the quantum analogs of certain symmetric polynomials…

For a 3D N=4 gauge theory, turning on the $\Omega$-background in RxR$^2_{\epsilon}$ deforms the Coulomb branch chiral ring into the quantum Coulomb branch algebra, generated by the 1/2-BPS monopoles together with the complex scalar in the…

To a quiver with involution, we study the Coulomb branch of the 3d $\mathcal{N} = 4$ involution-fixed part of the quiver gauge theory. We show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the…

A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both…

This paper provides the first algebraic characterization of an algebra of cohomological Hecke operators associated with modifications of coherent sheaves on a smooth surface $X$ along a fixed proper curve $Z \subset X$ (possibly singular…

This paper concerns the relation between the quantum toroidal algebras and the affine Yangians of $\mathfrak{sl}_n$, denoted by $\mathcal{U}^{(n)}_{q_1,q_2,q_3}$ and $\mathcal{Y}^{(n)}_{h_1,h_2,h_3}$, respectively. Our motivation arises…

We generalize the previously given algebraic version of "Feynman's proof of Maxwell's equations" to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such…

We extend previous work by developing a worldsheet description of non-abelian gauge theory (Yang-Mills). This task requires the introduction of Grassmann variables on the world sheet analogous to those of the Neveu-Schwarz-Ramond…

Let g be a complex, semisimple Lie algebra, and Y_h(g) and U_q(Lg) the Yangian and quantum loop algebra of g. Assuming that h is not a rational number and that q=exp(i \pi h), we construct an equivalence between the finite-dimensional…

We formulate shifted affine iquantum groups of arbitrary quasi-split ADE types via Drinfeld presentations. We construct GKLO-type representations of shifted affine iquantum groups via algebras of difference operators, which allow us to…

For non-abelian non-supersymmetric gauge theories, generic dual theories have been constructed. In these theories the couplings appear inverted. However, they do not possess a Yang-Mills structure but rather are a kind of non-linear sigma…

This is a first of our papers devoted to "noncommutative topology and graph theory". Its origin is the paper math.QA/0002238 by I. Gelfand, V. Retakh, and R.L. Wilson where a new class of noncommutative algebras $Q_n$ was introduced. The…

We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible…

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

Let $G$ be a complex reductive group and let $X$ and $E$ be two linear representations of $G$. Let $Y$ be a complete intersection in $X$ equal to the zero locus of a $G$-equivariant section of the trivial bundle $E \times X \to X$. We…

We describe a generalization of GKM theory for actions of arbitrary compact connected Lie groups. To an action satisfying the non-abelian GKM conditions we attach a graph encoding the structure of the non-abelian 1-skeleton, i.e., the…

We interpret the equivariant cohomology algebra H^*_{GL_n\times\C^*}(T^*F_\lambda;\C) of the cotangent bundle of a partial flag variety F_\lambda parametrizing chains of subspaces 0=F_0\subset F_1\subset\dots\subset F_N =\C^n, \dim…

The structure of equivariant cohomology in non-abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent BRST symmetry, and another nilpotent operator which restricts the…

We introduce parabolic presentations of twisted Yangians of types AI and AII, interpolating between the R-matrix presentation and the Drinfeld presentation. Then we formulate and provide parabolic presentations for the shifted twisted…

We consider the cohomological Hall algebra Y of a Lagrangian substack of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and its actions on the cohomology of quiver varieties. We conjecture that Y…