Eigenfunction Asymptotics in the Complex Domain for a Compact Lie Group
Abstract
Abstract Let $$(G,\kappa )$$ ( G , κ ) be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $$\tilde{G}$$ G ~ be the complexification of G . We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain operator kernels, which are defined in terms of the matrix elements of an irreducible representation drifting to infinity along a ray in weight space. These kernels are the equivariant components of Poisson and Szegő kernels on a fixed sphere bundle in $$\tilde{G}$$ G ~ , when the latter is identified with the tangent bundle of G in an appropriate way.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
advanced mathematical theories
Publication details
- Journal / source
- Journal of Geometric Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 5
- Publication date
- 10 April 2026
- Language
- EN