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 LG(n, 2n) and over the complex numbers the image is de fined, 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.
Lagrangian Grassmannians and Spinor Varieties in Characteristic Two / B. van Geemen, A. Marrani. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 15(2019).
|Titolo:||Lagrangian Grassmannians and Spinor Varieties in Characteristic Two|
VAN GEEMEN, LAMBERTUS (Primo) (Corresponding)
|Parole Chiave:||Lagrangian Grassmannian; spinor variety; characteristic two; Freudenthal triple system|
|Settore Scientifico Disciplinare:||Settore MAT/03 - Geometria|
|Data di pubblicazione:||2019|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.3842/SIGMA.2019.064|
|Appare nelle tipologie:||01 - Articolo su periodico|