Symmetry Integrability and Geometry-Methods and Applications | |
Lagrangian Grassmannians and Spinor Varieties in Characteristic Two | |
article | |
Bert van Geemen1  Alessio Marrani2  | |
[1] Dipartimento di Matematica, Università di Milano;Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi | |
关键词: Lagrangian Grassmannian; spinor variety; characteristic two; Freudenthal triple system; | |
DOI : 10.3842/SIGMA.2019.064 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
The vector space of symmetric matrices of size $n$ has a natural map to a projective space of dimension $2^n-1$ given by the principal minors. This map extends to the Lagrangian Grassmannian ${\rm LG}(n,2n)$ 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 ${\rm Spin}(2n+1)$. 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.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300000763ZK.pdf | 473KB | download |