Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
The vector space of symmetric matrices of size n has a natural map to a projective space of dimension 2ⁿ −1 given by the principal minors. This map extends to the Lagrangian Grassmannian LG(n, 2n), and over the complex numbers, the image is defined, as a set, by quartic equations. In case the charac...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210231 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two / B. van Geemen, A. Marrani // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 41 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The vector space of symmetric matrices of size n has a natural map to a projective space of dimension 2ⁿ −1 given by the principal minors. This map extends to the Lagrangian Grassmannian LG(n, 2n), and over the complex numbers, the image is defined, as a set, by quartic equations. In case the characteristic of the field is two, it was observed that, for n=3,4, the image is defined by quadrics. In this paper, we show that this is the case for any n and that, moreover, the image is the spinor variety associated to Spin(2n+1). Since some of the motivating examples are of interest in supergravity and in the black-hole/qubit correspondence, we conclude with a brief examination of other cases related to integral Freudenthal triple systems over integral cubic Jordan algebras.
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| ISSN: | 1815-0659 |