2025/07/24 by Gallivanone, Simone, Paoletti, Roberto
#FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2507.18285
Let (G,κ) be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let 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 irreducuble 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 G, when the latter is identified with the tangent bundle of G in an appropriate way.