Orbital theory for affine Lie algebras
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.
scientific article; zbMATH DE number 3873560
scientific article