相关论文: A new realization of quantum algebras in gauge the…

We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a…

We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of…

We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has…

We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and…

This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their…

We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several new identities in the quantized algebra, one of…

We introduce the notion of the ell-weight lattice and the ell-root lattice adapted to the study of finite-dimensional representations of quantum affine algebras. We then study the ell-weights of the fundamental representations and show that…

In \cite{FT19}, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated to certain 3D $N = 4$ quiver gauge theories. We describe a new…

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…

The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…

Let $\Gamma$ be a finite subgroup of $\SL_2(\C)$. We consider $\Gamma$-fixed point sets in Hilbert schemes of points on the affine plane $\C^2$. The direct sum of homology groups of components has a structure of a representation of the…

Let H be a Hopf algebra which is a finite module over a central sub-Hopf algebra R. The ramification behaviour of the maximal ideals of Z(H) with respect to the subalgebra R is studied. In the case when H is U(g), the enveloping algebra of…

Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of "degroupoidification": a…

We establish equivalences of derived categories of the following 3 categories: (1) Principal block of representations of the quantum at a root of 1; (2) G-equivariant coherent sheaves on the Springer resolution; (3) Perverse sheaves on the…

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on…

Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…

We formulate a two-parameter generalization of the geometric Langlands correspondence, which we prove for all simply-laced Lie algebras. It identifies the q-conformal blocks of the quantum affine algebra and the deformed W-algebra…

In this paper, we introduce and study shifted twisted quantum affine algebras which provide a twisted counterpart of the theory of shifted quantum affine algebras. The shifted twisted quantum affine algebra $\U_q^{\mu_+,\mu_-}(\hgs)$ is…