On Lagrangian Grassmannian Variety and Plücker Matrices - Jesús Carrillo-Pacheco (Mathematics, 2024)
The Plücker matrix <semantics>BL(n,E)</semantics> of the Lagrangian Grassmannian <semantics>L(n,E)</semantics>, is determined by the linear envelope <semantics>⟨L(n,E)⟩</semantics> of the Lagrangian Grassmannian. The linear envelope <semantics>⟨L(n,E)⟩</semantics> is the intersection of linear relations of Plücker of Lagrangian Grassmannian, defined here. The Plücker matrix <semantics>BL(n,E)</semantics> is a direct sum of the incidence matrix of the configuration of subsets. These matrices determine the isotropy index <semantics>rn</semantics> and <semantics>rn</semantics>-atlas which are invariants associated with the symplectic vector space E.