SPECTRAL UNIQUENESS OF BI-INVARIANT METRICS ON SYMPLECTIC GROUPS

In this short note, we prove that a bi-invariant Riemannian metric on Sp( n ) is uniquely determined by the spectrum of its Laplace–Beltrami operator within the class of left-invariant metrics on Sp( n ). In other words, on any of these compact simple Lie groups, every left-invariant metric which is...

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Bibliographic Details
Published inTransformation groups Vol. 24; no. 4; pp. 1157 - 1164
Main Author LAURET, EMILIO A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2019
Springer Nature B.V
Subjects
Algebra
Invariants
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
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Summary:In this short note, we prove that a bi-invariant Riemannian metric on Sp( n ) is uniquely determined by the spectrum of its Laplace–Beltrami operator within the class of left-invariant metrics on Sp( n ). In other words, on any of these compact simple Lie groups, every left-invariant metric which is not right-invariant cannot be isospectral to a bi-invariant metric. The proof is elementary and uses a very strong spectral obstruction proved by Gordon, Schueth and Sutton.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-018-9486-5