Inverse spectral results for non-abelian group actions
Name
2001.08305.pdf
Description
Submitted version
Size
394.15 KB
Format
Adobe PDF
Checksum (MD5)
7a8918a44ae874d7218da67bfbf17a4e
Author(s)
Guillemin, Victor
Wang, Zuoqin
Date Issued
2021
Journal
Indagationes Mathematicae
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2020 Royal Dutch Mathematical Society (KWG) In this paper we will extend to non-abelian groups inverse spectral results, proved by us in an earlier paper (Guillemin and Wang, 2016), for compact abelian groups, i.e. tori. More precisely, Let G be a compact Lie group acting isometrically on a compact Riemannian manifold X. We will show that for the Schrödinger operator −ħ2Δ+V with V∈C∞(X)G, the potential function V is, in some interesting examples, determined by the G-equivariant spectrum. The key ingredient in this proof is a generalized Legendrian relation between the Lagrangian manifolds Graph(dV) and Graph(dF), where F is a spectral invariant defined on an open subset of the positive Weyl chamber.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.INDAG.2020.05.004
