Related papers: BFN Springer Theory
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant…
We specify the conjecture about the structure of the Coulomb branch of N=2 supersymmetric quantum field theories in four dimensions.
An extension of the Lorentz group that includes generators $\Gamma^\mu$ carrying a space-time index has been previously demonstrated to \emph{explicitly} construct the Minkowski metric \emph{within} the internal group space as a consequence…
In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann…
We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional $\mathcal{N} = 4$ abelian gauge theories that have superconformal infrared limits.…
We study the hemisphere partition function of a three-dimensional $\mathcal{N}=4$ supersymmetric $U(N)$ gauge theory with one adjoint and one fundamental hypermultiplet -- the ADHM quiver theory. In particular, we propose a distinguished…
Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant cohomology of Springer fibers for $GL_n(\mathbb{C})$ using…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…
We consider Iwahori-Coulomb branches $\mathcal{A}_{G,\mathbf{N},\mathbf{V}}^{\mathrm{Fl}}$, which are the affine flag analogs of the original Coulomb branches $\mathcal{A}_{G,\mathbf{N}}^{\mathrm{Gr}}$ defined by Braverman, Finkelberg, and…
In this note we show that the multiplicative Grothendieck-Springer space has a natural quasi-Poisson structure. The associated group-valued moment map is the resolution morphism, and the quasi-Hamiltonian leaves are the connected components…
The aim of this paper is to extend existence results for the Coulomb gauge from standard gauge theory to a non-associative setting. Non-associative gauge theory is based on smooth loops, which are the non-associative analogs of Lie groups.…
Let Gr be the affine Grassmannian for a connected complex reductive group G. Let C_G be the complex vector space spanned by (equivalence classes of) Mirkovic-Vilonen cycles in Gr. The Beilinson-Drinfeld Grassmannian can be used to define a…
We study ring of functions on the (classical and quantized) phase space of 2-dimensional BF theory with the gauge group $\mathrm{GL}_N$ coupled to a 1-dimensional quantum mechanics with global symmetry $\mathrm{GL}_K$. These functions are…
Obtaining the classification of 3d $\mathcal{N}=4$ quivers whose Coulomb branches have an isolated singularity is an essential step in understanding moduli spaces of vacua of supersymmetric field theories with 8 supercharges in any…
Let $H$ be a quasitriangular quasi-Hopf algebra, we construct a braided group $\underline{H}$ in the quasiassociative category of left $H$-modules. Conversely, given any braided group $B$ in this category, we construct a quasi-Hopf algebra…
In Kapranov, M. {\it Noncommutative geometry based on commutator expansions,} J. reine angew. Math {\bf 505} (1998) 73-118, a theory of noncommutative algebraic varieties was proposed. Here we prove a structure theorem for the…
We give the analogue for Hopf algebras of the polyuble Lie bialgebra construction by Fock and Rosli. By applying this construction to the Drinfeld-Jimbo quantum group, we obtain a deformation quantization $\mathbb{C}_\hslash[(N \backslash…
We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a…
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex…
The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of 2-dimensional sigma models as…