Localization of valuations and Alesker's irreducibility theorem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912733866229760 |
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| author | Hofstätter, Georg C. Knoerr, Jonas |
| author_facet | Hofstätter, Georg C. Knoerr, Jonas |
| contents | We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are representable by integration with respect to the normal cycle. This allows us to reduce the statement to a corresponding result for the representation of $\mathfrak{sl}(n)$ on the space of these differential forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization of valuations and Alesker's irreducibility theorem Hofstätter, Georg C. Knoerr, Jonas Metric Geometry Differential Geometry Representation Theory 52B45, 53C65, 43A75 We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are representable by integration with respect to the normal cycle. This allows us to reduce the statement to a corresponding result for the representation of $\mathfrak{sl}(n)$ on the space of these differential forms. |
| title | Localization of valuations and Alesker's irreducibility theorem |
| topic | Metric Geometry Differential Geometry Representation Theory 52B45, 53C65, 43A75 |
| url | https://arxiv.org/abs/2510.25698 |