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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2306.09047 |
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| _version_ | 1866910313009381376 |
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| author | Lavicka, Roman |
| author_facet | Lavicka, Roman |
| contents | It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to the classical theory on the Euclidean space R^{m} unless the superdimension M:=m-2n is even and non-positive. The underlying symmetry is given by the orthosymplectic superalgebra osp(m|2n). In this paper, when the symmetry is reduced to osp(m-1|2n) we describe explicitly the corresponding branching laws for spherical harmonics on R^{m|2n} also in exceptional cases. In unexceptional cases, these branching laws are well-known and quite analogous as in the Euclidean framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09047 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Branching laws for spherical harmonics on superspaces in exceptional cases Lavicka, Roman Complex Variables Mathematical Physics Representation Theory 30G35, 17B10, 58C50 It turns out that harmonic analysis on the superspace R^{m|2n} is quite parallel to the classical theory on the Euclidean space R^{m} unless the superdimension M:=m-2n is even and non-positive. The underlying symmetry is given by the orthosymplectic superalgebra osp(m|2n). In this paper, when the symmetry is reduced to osp(m-1|2n) we describe explicitly the corresponding branching laws for spherical harmonics on R^{m|2n} also in exceptional cases. In unexceptional cases, these branching laws are well-known and quite analogous as in the Euclidean framework. |
| title | Branching laws for spherical harmonics on superspaces in exceptional cases |
| topic | Complex Variables Mathematical Physics Representation Theory 30G35, 17B10, 58C50 |
| url | https://arxiv.org/abs/2306.09047 |