Related papers: Twisted quantum affine algebras and equivariant $\…

For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of $V_Q$. In this paper we classify the…

In this paper we generalize Drinfeld's twisted quantum affine algebras to construct twisted quantum algebras for all simply-laced generalized Cartan matrices and present their vertex representation realizations.

Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof--Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $\phi$-coordinated…

In this paper, we present a canonical association of quantum vertex algebras and their $\phi$-coordinated modules to Lie algebra $\gl_{\infty}$ and its 1-dimensional central extension. To this end we construct and make use of another…

We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of…

In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted…

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras…

In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $\phi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras,…

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…

Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…

For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra $V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of $V_{\mathcal{E}}(\ell)$ equipped with…

In this paper, we explore a canonical connection between the algebra of $q$-difference operators $\widetilde{V}_{q}$, affine Lie algebra and affine vertex algebras associated to certain subalgebra $\mathcal{A}$ of the Lie algebra…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

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…

In this paper, we explore natural connections among the representations of the extended affine Lie algebra $\widehat{sl_N}(\mathbb{C}_q)$ with $\mathbb{C}_q=\mathbb{C}_q[t_0^{\pm1},t_1^{\pm1}]$ an irrational quantum 2-torus, the simple…

Let $\mathfrak g$ be a finite simple Lie algebra, and let $r$ denote the ratio of the square length of long roots to that of short roots. Let $\wp>2r$ be an integer and $\zeta$ a primitive $\wp$-th root of unity. Denote by $\mathcal…

To give a unified treatment on the association of Lie algebras and vertex algebras, we study $(G,\chi_\phi)$-equivariant $\phi$-coordinated quasi modules for vertex algebras, where $G$ is a group with $\chi_\phi$ a linear character of $G$…

Let $\Gamma$ be a generic subgroup of the multiplicative group $\mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $\Gamma$, called twisted $\Gamma$-Lie algebras, which is a natural generalization of…

For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…

We study $\N$-graded $\phi$-coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $\widetilde{A}(V)$ introduced by Y.-Z. Huang. Among the main results, we establish a bijection…