Remarks on Diffeological Frobenius Reciprocity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918331481587712 |
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| author | Barbieri, Gabriele Watts, Jordan Ziegler, Francois |
| author_facet | Barbieri, Gabriele Watts, Jordan Ziegler, Francois |
| contents | A recent paper [R22] established "Frobenius reciprocity" as a bijection $t$ between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1°) $t$ is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2°) $t$ respects the reduced diffeological $2$-forms they may (or might not) carry. In this paper, we prove both this conjecture and a similar one on prequantum reduction, and also give new sufficient conditions for the reduced forms to exist. We stop short of proving that they always exist. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_03927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on Diffeological Frobenius Reciprocity Barbieri, Gabriele Watts, Jordan Ziegler, Francois Symplectic Geometry Representation Theory 53D20, 53D10, 53D50, 58A10, 58A40, 22D30 A recent paper [R22] established "Frobenius reciprocity" as a bijection $t$ between certain symplectically reduced spaces (which need not be manifolds), and conjectured: 1°) $t$ is a diffeomorphism when these spaces are endowed with their natural subquotient diffeologies, 2°) $t$ respects the reduced diffeological $2$-forms they may (or might not) carry. In this paper, we prove both this conjecture and a similar one on prequantum reduction, and also give new sufficient conditions for the reduced forms to exist. We stop short of proving that they always exist. |
| title | Remarks on Diffeological Frobenius Reciprocity |
| topic | Symplectic Geometry Representation Theory 53D20, 53D10, 53D50, 58A10, 58A40, 22D30 |
| url | https://arxiv.org/abs/2403.03927 |