Orbital theory for affine Lie algebras
type: Item
instance of: scholarly article
title: Orbital theory for affine Lie algebras
zbMATH Open document ID: 0548.17007
DOI: 10.1007/BF01388449
published in: Inventiones Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143148
review text: The paper develops an orbit method for the infinite dimensional Lie algebras called ''affine''. The main results are the infinite dimensional analogues of the intertwining property of the invariant integral and the Fourier transforms on a semisimple Lie algebra and a Cartan subalgebra of compact type and the related Kirillov type formula for characters as orbital integrals. Because of the infinite dimensionality of the Lie algebras the author has to develop methods from infinite dimensional analysis new in this context, applying in particular the Floquet theory of linear differential equations with periodic coefficients, the theory of the heat equation on Lie groups, and the theories of Gaussian and Wiener measures and Brownian motion.
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 3873560
zbMATH Keywords: Gaussian measures
zbMATH Keywords: affine Lie algebras
zbMATH Keywords: orbit method
zbMATH Keywords: intertwining property
zbMATH Keywords: invariant integral
zbMATH Keywords: Fourier transforms
zbMATH Keywords: Kirillov type formula for characters
zbMATH Keywords: Floquet theory
zbMATH Keywords: heat equation
zbMATH Keywords: Wiener measures
zbMATH Keywords: Brownian motion
author: Igor B. Frenkel
MaRDI profile type: Publication
cites work: Q4175791
cites work: Product integration of measures and applications
cites work: Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold
cites work: The Heat Equation on a Compact Lie Group
cites work: Basic representations of affine Lie algebras and dual resonance models
cites work: Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
cites work: Dedekind's η-function and the cohomology of infinite dimensional Lie algebras
cites work: The arithmetic theory of loop algebras
cites work: The arithmetic theory of loop groups
cites work: Lie algebra homology and the Macdonald-Kac formulas
cites work: Q4144425
cites work: Integration in Functional Spaces and its Applications in Quantum Physics
cites work: Differential Operators on a Semisimple Lie Algebra
cites work: Q5330830
cites work: Brownian motions in a Lie group
cites work: SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH
cites work: Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
cites work: Q4109839
cites work: On Macdonald's \(\eta\)-function formula, the Laplacian and generalized exponents
cites work: Gaussian measures in Banach spaces
cites work: Root systems and elliptic curves
cites work: Affine root systems and Dedekind's \(\eta\)-function
cites work: Q5585820
cites work: A new class of Lie algebras
cites work: The Feynman maps and the Wiener integral
cites work: Harmonic analysis on real reductive groups
cites work: On Rossmann's character formula for discrete series
cites work: Q5332803
cites work: Q3233674
cites work: Q3229429
cites work: Q5522602
OpenAlex ID: W2014558193
description: scientific article; zbMATH DE number 3873560