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Mathematics > Representation Theory

arXiv:2212.00713 (math)
[Submitted on 1 Dec 2022 (v1), last revised 30 Jun 2023 (this version, v2)]

Title:Analytic, Differentiable and Measurable Diagonalizations in Symmetric Lie Algebras

Authors:Emanuel Malvetti, Gunther Dirr, Frederik vom Ende, Thomas Schulte-Herbrüggen
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Abstract:We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix diagonalization, such as the eigenvalue decomposition of real symmetric or complex Hermitian matrices, and the real or complex singular value decomposition. Concretely, given a path of structured matrices with a certain smoothness, we study what kind of smoothness one can obtain for the corresponding diagonalization of the matrices.
Comments: 62 pages, changed numbering
Subjects: Representation Theory (math.RT)
MSC classes: 15A20 (Primary) 17B20 (Secondary)
Cite as: arXiv:2212.00713 [math.RT]
  (or arXiv:2212.00713v2 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.2212.00713

Submission history

From: Emanuel Malvetti [view email]
[v1] Thu, 1 Dec 2022 18:15:43 UTC (182 KB)
[v2] Fri, 30 Jun 2023 19:17:05 UTC (182 KB)
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