Upper block triangular form for the Laplace-Beltrami operator on the special orthogonal group acquired through a flag of trace polynomials spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866914031290286080 |
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| author | Birtea, Petre Casu, Ioan Comanescu, Dan |
| author_facet | Birtea, Petre Casu, Ioan Comanescu, Dan |
| contents | The Laplacian of a general trace polynomial function defined on the special orthogonal group $SO(N)$ is explicitly computed. An invariant flag of spaces generated by trace polynomials is constructed. The matrix of the Laplace-Beltrami operator on $SO(N)$ for this flag of vector spaces takes an upper block triangular form. As a consequence of this construction, the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on $SO(N)$ can be computed in an iterative manner. For the particular cases of the special orthogonal groups $SO(3)$ and $SO(4)$ the complete list of eigenvalues is obtained and the corresponding irreducible characters of the representation for these groups are expressed as trace polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_08391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper block triangular form for the Laplace-Beltrami operator on the special orthogonal group acquired through a flag of trace polynomials spaces Birtea, Petre Casu, Ioan Comanescu, Dan Mathematical Physics 15B10, 53Bxx, 58Cxx, 33C55, 42Cxx, 43Axx, 20Cxx The Laplacian of a general trace polynomial function defined on the special orthogonal group $SO(N)$ is explicitly computed. An invariant flag of spaces generated by trace polynomials is constructed. The matrix of the Laplace-Beltrami operator on $SO(N)$ for this flag of vector spaces takes an upper block triangular form. As a consequence of this construction, the eigenvalues and eigenfunctions of the Laplace-Beltrami operator on $SO(N)$ can be computed in an iterative manner. For the particular cases of the special orthogonal groups $SO(3)$ and $SO(4)$ the complete list of eigenvalues is obtained and the corresponding irreducible characters of the representation for these groups are expressed as trace polynomials. |
| title | Upper block triangular form for the Laplace-Beltrami operator on the special orthogonal group acquired through a flag of trace polynomials spaces |
| topic | Mathematical Physics 15B10, 53Bxx, 58Cxx, 33C55, 42Cxx, 43Axx, 20Cxx |
| url | https://arxiv.org/abs/2509.08391 |