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 |
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| Format: | Artikel |
| Sprache: | Englisch |
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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| _version_ | 1862720295283982336 |
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| author | van Geemen, B. Marrani, A. |
| author_facet | van Geemen, B. Marrani, A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-07T21:24:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210231 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:50Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | van Geemen, B. Marrani, A. 2025-12-04T13:04:22Z 2019 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. 1815-0659 2010 Mathematics Subject Classification: 14M17; 20G15; 51E25 arXiv: 1903.01228 https://nasplib.isofts.kiev.ua/handle/123456789/210231 https://doi.org/10.3842/SIGMA.2019.064 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. BvG would like to thank L. Oeding and W. van der Kallen for helpful correspondence and discussions. We are indebted to the referees of this paper for comments and suggestions for improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lagrangian Grassmannians and Spinor Varieties in Characteristic Two Article published earlier |
| spellingShingle | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two van Geemen, B. Marrani, A. |
| title | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two |
| title_full | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two |
| title_fullStr | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two |
| title_full_unstemmed | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two |
| title_short | Lagrangian Grassmannians and Spinor Varieties in Characteristic Two |
| title_sort | lagrangian grassmannians and spinor varieties in characteristic two |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210231 |
| work_keys_str_mv | AT vangeemenb lagrangiangrassmanniansandspinorvarietiesincharacteristictwo AT marrania lagrangiangrassmanniansandspinorvarietiesincharacteristictwo |