Аннотация:
Let LG(n,V) denote the Lagrangian Grassmannian of a symplectic
vector space V of dimension 2n. What is the "correct" projective space into
which LG(n,V) embeds?
By correct we mean non-degeneracy: No hyperplane should contain the image
of the embedding.
In characteristic zero, the desired projective space is simply the subspace
of the projective n-th exterior power of V for which interior
multiplication with the symplectic form vanishes.
In positive characteristic, it turns out that this embedding is in general
degenerate.
Nondegeneracy is important for construct linear error correcting codes
associated with LG_n(V) over finite fields. We determine the 'correct'
subspace by developing an analogue -for the case of positive
characteristic- of the classical Lepage decomposition of the exterior
algebra of V (used for example in the context of Monge-Ampere type PDEs).
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