Integrals of motion and quantum groups

  title={Integrals of motion and quantum groups},
  author={Boris Feigin and Edward Frenkel},
  journal={Lecture Notes in Mathematics},
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of certain complexes, which are modeled on the BGG resolutions of the associated Lie algebras and their quantum deformations. This way we prove that all classical integrals of motion can be quantized. For the Toda field theories associated to finite-dimensional Lie algebras, the algebra of integrals of… 

Quantum Toroidal Comodule Algebra of Type An−1 and Integrals of Motion

. We introduce an algebra K n which has a structure of a left comodule over the quantum toroidal algebra of type A n − 1 . Algebra K n is a higher rank generalization of K 1 , which provides a

Quantum cohomology of flag manifolds and Toda lattices

We discuss relations of Vafa's quantum cohomology with Floer's homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of


We discuss relations of Vafa’s quantum cohomology with Floer’s homology theory, introduce equivariant quantum cohomology, formulate some conjectures about its general properties and, on the basis of

The Intergals of Motion for

We introduce three parameter deformation of W -algebra W (d slN) and its screening currents, which is realized by direct sum of the deformed W -algebra Wq,t(d slN) and proper bosonic algebra. We

The Quantization of the Generalized mKdV Equations for ŝl 2

We construct quantum deformations of the integrals of motion of the generalized mKdV equations for sl 2. For this, we give the relevant vertex operator algebra and prove quantum Serre relations for

The Integrals of Motion for the Deformed Virasoro Algebra

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed Virasoro algebra. We call one of them local integrals and the other nonlocal one, since they can

Infinite Abelian Subalgebras in Quantum W-Algebras: An Elementary Proof

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Differential calculi on some quantum prehomogeneous vector spaces

This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the

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Spin and wedge representations of infinite-dimensional Lie algebras and groups.

  • V. KacD. Peterson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1981
A construction of all level-one highest-weight representations of orthogonal affine Lie algebras in terms of creation and annihilation operators on an infinite-dimensional Grassmann algebra is deduced.

W -Algebras and Langlands-Drinfeld Correspondence

The W-algebras, associated to arbitrary simple Lie algebras, are defined as the cohomologies of certain BRST complexes. This allows to prove many important facts about them, such as determinant

Representations of affine Kac-Moody algebras, bosonization and resolutions

We study boson representations of the affine Kac-Moody algebras and give an explicit description of primary fields and intertwining operators, using vertex operators. We establish the resolution of

Fock representations and BRST cohomology inSL(2) current algebra

We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of