相关论文: Virtual Coulomb branch and vertex functions

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties. This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras…

We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the…

We introduce twisted quantum $K$-rings, defined via twisted $K$-theoretic Gromov-Witten invariants. We develop a toolkit for computing relations by adapting some results about ordinary quantum K rings to our setting, and discuss some…

We introduce quiver representation-valued invariants of oriented virtual knots and links associated to a choice of finite virtual biquandle, abelian group, set of virtual Boltzmann weights, commutative unital ring and set of virtual…

We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which we partially prove. We propose a construction of…

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 consider asymptotic limits of q-oscillator (or Heisenberg) realizations of Verma modules over the quantum superalgebra $U_{q}(gl(M|N))$, and obtain q-oscillator realizations of the contracted algebras proposed in [arXiv:1205.1471].…

We derive, from first principles, the complete Luttinger liquid theory of abelian quantum Hall edge states. This theory includes the effects of disorder and Coulomb interactions as well as the coupling to external electromagnetic fields. We…

In previous work we have shown that the equivariant index of multi-centered N=2 black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and…

We discuss a class of quantum vertex algebras where not only the commutativity of the vertex algebra is broken by a braiding map $S^{(\tau)}$, but also the translation covariance is broken by a translation map $S^{(\gamma)}$. The new class…

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 prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…

We study transverse equivariant Hilbert schemes of affine hypertoric varieties equipped with a symplectic action of a Weyl group. In particular, we show that the Coulomb branches of Braverman, Finkelberg, and Nakajima can be obtained either…

Let $\cl{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $\mathcal{A}(\Omega)$, where $\Omega \subseteq \bb{C}^m$ is a bounded domain. Let $\cl{M}_0\subseteq \cl{M}$ be the submodule of functions vanishing…

We state a wall-crossing formula for the virtual classes of epsilon-stable quasimaps to GIT quotients and prove it for complete intersections in projective space, with no positivity restrictions on their first Chern class. As a consequence,…

The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The…

In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology…

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…

By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…

For each non-constant $q$ in the set of $n$-variable Boolean functions, the {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of…