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New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)

MPS-Authors
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Gudmundsson,  Sigmundur
Max Planck Institute for Mathematics, Max Planck Society;

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Siffert,  Anna
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Gudmundsson, S., & Siffert, A. (2021). New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n). The Journal of Geometric Analysis, 31(1), 250-281. doi:10.1007/s12220-019-00259-3.


Cite as: http://hdl.handle.net/21.11116/0000-0006-9E3F-3
Abstract
We develope a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group $SU(n)$. We then show that the special orthogonal group $SO(n)$ and the quaternionic unitary group $Sp(n)$ fall into the scheme. As a by-product we obtain new harmonic morphisms on these groups. All the constructed maps are defined on open and dense subsets of the corresponding spaces.