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Related papers: Twisted Vertex Operators and A-D-E Representations

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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…

Quantum Algebra · Mathematics 2026-04-07 Naihuan Jing , Fei Kong , Haisheng Li , Shaobin Tan

We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.

Quantum Algebra · Mathematics 2007-05-23 Haisheng Li

The usual vertex algebras have as underlying symmetry the Hopf algebra $H_D=\mathbb C[D]$ of infinitesimal translations. We show that it is possible to replace $H_D$ by another symmetry algebra $H_T=\mathbb C[T,T\inv]$, the group algebra of…

Quantum Algebra · Mathematics 2007-05-23 Maarten J Bergvelt

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…

q-alg · Mathematics 2009-10-30 J. F. Cornwell

Twisted modules for N=2 supersymmetric vertex operator superalgebras are classified for the vertex operator superalgebra automorphisms which are lifts of a finite automorphism of the N=2 Neveu-Schwarz Lie superalgebra representation. These…

Quantum Algebra · Mathematics 2013-04-16 Katrina Barron

The aim of this work is focused on linearizing and found the Lax Pairs of the algebraic complete integrability (a.c.i) Toda lattice associated with the twisted affine Lie algebra \(a_4^{\left(2\right)}\). Firstly, we recall that our case of…

Exactly Solvable and Integrable Systems · Physics 2025-01-07 Bruce Lionnel Lietap Ndi , Djagwa Dehainsala , Joseph Dongho

We study numerically the ODE/IM correspondence for untwisted affine Lie algebras associated with simple Lie algebras including exceptional type. We consider the linear problem obtained from the massless limit of that of the modified affine…

High Energy Physics - Theory · Physics 2020-12-15 Katsushi Ito , Takayasu Kondo , Kohei Kuroda , Hongfei Shu

This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting…

Quantum Algebra · Mathematics 2007-05-23 Pavel Etingof , David Kazhdan

On the vertex operator algebra associated with rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of…

Quantum Algebra · Mathematics 2020-09-08 Wuxing Cai , Naihuan Jing

Let $L$ be an even lattice without roots. In this article, we classify all Ising vectors in the vertex operator algebra $V_L^+$ associated with $L$.

Quantum Algebra · Mathematics 2012-02-29 Hiroki Shimakura

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

solv-int · Physics 2009-10-30 Y. Brihaye , S. Giller , P. Kosinski , J. Nuyts

Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…

Representation Theory · Mathematics 2007-05-23 Johan van de Leur

The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.

Quantum Algebra · Mathematics 2015-01-05 Chongying Dong , Feng Xu , Nina Yu

In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.

Logic · Mathematics 2019-10-24 Guido Gherardi , Alberto Marcone , Arno Pauly

In this paper, we provide a unified approach to study the cohomology theories and deformation theories of various types of operators in the category of Lie algebras, including modified $r$-matrices, crossed homomorphisms, derivations,…

Mathematical Physics · Physics 2024-05-07 Jun Jiang , Yunhe Sheng , Rong Tang

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…

Representation Theory · Mathematics 2007-05-23 Vyjayanthi Chari , Adriano Moura

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the…

Strongly Correlated Electrons · Physics 2009-11-07 Masaaki Nakamura , Johannes Voit

Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a…

Strongly Correlated Electrons · Physics 2025-08-28 Bram Vancraeynest-De Cuiper , Clement Delcamp

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…

Rings and Algebras · Mathematics 2022-05-03 Masaki Matsuno