Affine Kac-Moody algebras and semi-infinite flag manifolds
type: Item
instance of: scholarly article
title: Affine Kac-Moody algebras and semi-infinite flag manifolds
zbMATH Open document ID: 0722.17019
DOI: 10.1007/BF02097051
published in: Communications in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: With the technique of semi-infinite cohomology over (affine) Kac-Moody algebras the authors realize so-called Wakimoto modules as twisted Verma modules. Among other wonders this brings about a two-sided resolution of these twisted Verma modules leading to a semi-infinite analog of the Borel-Weil-Bott theorem. The exposition is highly illuminating and equally breezy (lots of details are to be published).
reviewed by: Dimitry Leites
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 4189983
zbMATH Keywords: representations
zbMATH Keywords: conformal field theory
zbMATH Keywords: semi-infinite forms
zbMATH Keywords: flag manifolds
zbMATH Keywords: semi-infinite cohomology
zbMATH Keywords: Kac-Moody algebras
zbMATH Keywords: Wakimoto modules
zbMATH Keywords: twisted Verma modules
author: B. Feigin
author: Edward Frenkel
MaRDI profile type: Publication
cites work: Q3688545
cites work: Q3933105
cites work: Wave equation scattering in even-dimensional spaces
cites work: Q4107261
cites work: Kählerian Coset Spaces of Semisimple Lie Groups
cites work: Homogeneous vector bundles
cites work: Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
cites work: Q3688825
cites work: Structure of some categories of representations of infinite-dimensional Lie algebras
cites work: Q3333210
cites work: Q3804867
cites work: Q3804870
cites work: Representations of affine Kac-Moody algebras, bosonization and resolutions
cites work: Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds
cites work: Lie algebra homology and the Macdonald-Kac formulas
cites work: Sugawara operators and Kac-Kazhdan conjecture
cites work: Infinite dimensional Lie algebras. An introduction
cites work: Structure of representations with highest weight of infinite-dimensional Lie algebras
cites work: Q3027260
cites work: Spin and wedge representations of infinite-dimensional Lie algebras and groups
cites work: Superconformal current algebras and their unitary representations
cites work: Representations of Coxeter groups and Hecke algebras
cites work: Q3910633
cites work: The Grothendieck-Cousin complex of an induced representation
cites work: The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
cites work: Spectrum of infinite-dimensional Banach spaces
cites work: Singular vectors in Verma modules over affine algebras
cites work: Infinite flag varieties and conjugacy theorems
cites work: Q3754832
cites work: Residues of differentials on curves
cites work: Fock space representations of the Virasoro algebra. Intertwining operators
cites work: Fock representations of the affine Lie algebra \(A_ 1^{(1)}\)
cites work: A class of non-standard modules for affine Lie algebras
cites work: Hidden SL(n) symmetry in conformal field theories
full work available at URL: https://doi.org/10.1007/bf02097051
OpenAlex ID: W2070288700
Recommended article: Q4027539
Recommended article: Semi-infinite Schubert varieties and quantum \(K\)-theory of flag manifolds
Recommended article: D-modules on the affine flag variety and representations of affine Kac-Moody algebras
Recommended article: Q3333210
Recommended article: The semi-infinite homology of Kac-Moody and Virasoro Lie algebras
Recommended article: Q3701600
Recommended article: Varieties of affine Kac-Moody algebras
Recommended article: Borel-Weil-type theorem for the flag manifold of a generalized Kac-Moody algebra
Recommended article: Equivariant \(K\)-theory of affine flag manifolds and affine Grothendieck polynomials
Recommended article: Borel-Weil type theorem for the flag manifold of a generalized Kac-Moody algebra
description: scientific article; zbMATH DE number 4189983