On Generalized Pfaffians
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913496914984960 |
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| author | Distler, Jacques Donagi, Nathan Donagi, Ron |
| author_facet | Distler, Jacques Donagi, Nathan Donagi, Ron |
| contents | The determinant of an anti-symmetric matrix $g$ is the square of its Pfaffian, which like the determinant is a polynomial in the entries of $g$. Studies of certain super conformal field theories (of class S) suggested a conjectural generalization of this, predicting that each of a series of other polynomials in the entries of $g$ also admit polynomial square roots. Among other consequences, this conjecture led to a characterization of the local Hitchin image for type D. Several important special cases had been established previously. In this paper we prove the conjecture in full. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Generalized Pfaffians Distler, Jacques Donagi, Nathan Donagi, Ron Algebraic Geometry High Energy Physics - Theory Combinatorics The determinant of an anti-symmetric matrix $g$ is the square of its Pfaffian, which like the determinant is a polynomial in the entries of $g$. Studies of certain super conformal field theories (of class S) suggested a conjectural generalization of this, predicting that each of a series of other polynomials in the entries of $g$ also admit polynomial square roots. Among other consequences, this conjecture led to a characterization of the local Hitchin image for type D. Several important special cases had been established previously. In this paper we prove the conjecture in full. |
| title | On Generalized Pfaffians |
| topic | Algebraic Geometry High Energy Physics - Theory Combinatorics |
| url | https://arxiv.org/abs/2409.06871 |