Эта публикация цитируется в
1 статье
Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
Bert van Geemena,
Alessio Marranibcd a Dipartimento di Matematica, Università di Milano, Via Saldini 50, I-20133 Milano, Italy
b Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi,
Via Panisperna 89A, I-00184, Roma, Italy
c INFN, sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
d Dipartimento di Fisica "Galileo Galilei", Università degli studi di Padova, I-35131 Padova, Italy
Аннотация:
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.
Ключевые слова:
Lagrangian Grassmannian, spinor variety, characteristic two, Freudenthal triple system.
MSC: 14M17,
20G15,
51E25 Поступила: 8 марта 2019 г.; в окончательном варианте
21 августа 2019 г.; опубликована
27 августа 2019 г.
Язык публикации: английский
DOI:
10.3842/SIGMA.2019.064