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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.02499 |
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| _version_ | 1866914737655119872 |
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| author | Mohammadpour, Mozhgan Waldron, Shayne |
| author_facet | Mohammadpour, Mozhgan Waldron, Shayne |
| contents | We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs. This is done by developing the general theory of complex designs and associated (harmonic) Molien series for group actions. As an application, we give explicit constructions of some putatively optimal real and complex spherical t-designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complex spherical designs from group orbits Mohammadpour, Mozhgan Waldron, Shayne Combinatorics Group Theory 05B30, 42C15, 65D30, 94A12 We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs. This is done by developing the general theory of complex designs and associated (harmonic) Molien series for group actions. As an application, we give explicit constructions of some putatively optimal real and complex spherical t-designs. |
| title | Complex spherical designs from group orbits |
| topic | Combinatorics Group Theory 05B30, 42C15, 65D30, 94A12 |
| url | https://arxiv.org/abs/2308.02499 |