2019
DOI: 10.3842/sigma.2019.064
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Lagrangian Grassmannians and Spinor Varieties in Characteristic Two

Abstract: 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 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 … Show more

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Cited by 5 publications
(6 citation statements)
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“…The matrix q can therefore be put in the form 13) with one vanishing row and one vanishing column. In this basis, the diagonal D term corresponding to the bottom right entry has the form 1 15) with no sum over a and no q fields. This D term has no vanishing solutions for r 0, hence there can be no Higgs phase for r 0 if k is odd.…”
Section: Jhep10(2020)200mentioning
confidence: 99%
“…The matrix q can therefore be put in the form 13) with one vanishing row and one vanishing column. In this basis, the diagonal D term corresponding to the bottom right entry has the form 1 15) with no sum over a and no q fields. This D term has no vanishing solutions for r 0, hence there can be no Higgs phase for r 0 if k is odd.…”
Section: Jhep10(2020)200mentioning
confidence: 99%
“…The bijection induced by the Lagrangian mapping between subspaces of maximal dimension of W(2n − 1, 2) and points of Z n was already established in [12] in order to generalize observations made in [16] regarding the n = 3 case and its connection with the socalled black-holes/qubits correspondence. More recently, that same bijection was also considered in [26] with motivating examples from supergravity theory. It was proven that over F 2 , Z n is the image of the Spinor variety and thus a Spin(2n + 1)-orbit.…”
Section: Introductionmentioning
confidence: 85%
“…consisting of any number of reflections inside the canonical coordinate 2-planes {e −i , e i−1 } i=1,...,N , since it leaves invariant the Plücker coordinates π λ (w 0 ) for all symmetric partitions λ = λ T . In fact, the converse is also true [34]; two elements of Gr L V (H N , ω N ) have the same image under the Lagrange map if and only if they lie on the same (Z 2 ) N orbit. Generically, (Z 2 ) N has the 2-element subgroup {±I 2N } as stability subgroup, and there is an open dense stratum in which all the orbits have 2 N −1 elements.…”
Section: Inverse Of the Lagrange Mapmentioning
confidence: 94%
“…However, the map L is not one-to-one (cf. [34]). As explained in Section 2.7 its fibres are the orbits of the group (Z 2 ) N of reflections within the symplectic 2-planes corresponding to a canonical basis and, generically, are of cardinality 2 N −1 .…”
Section: Integrable Hierarchies Grassmannians τ -Functionsmentioning
confidence: 99%