منابع مشابه
Unitary Grassmannians
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.
متن کاملUnitary Grassmannians of Division Algebras
We consider a central division algebra over a separable quadratic extension of a base field endowed with a unitary involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. The remaining related projective homogeneous varieties are shown to be 2-compressible in general. Together with [17], where a similar issue for orthogonal and symplectic involuti...
متن کاملOperations on Subspaces in Real Unitary Space
Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 + W2 yields a strict subspace of V and is defined as follows: (Def. 1) The carrier of W1 + W2 = {v + u; v ranges over vectors of V , u ranges over vectors of V : v ∈ W1 ∧ u ∈ W2}. Let V be a real unitary space and let W1, W2 be subspaces of V . The functor W1 ∩ W2 yields a strict subspace of V and is defined by: (De...
متن کاملSubspaces and Cosets of Subspace of Real Unitary Space
Let V be a real unitary space. A real unitary space is said to be a subspace of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the zero of it = the zero of V , (iii) the addition of it = (the addition of V )↾[: the carrier of it, the carrier of it :], (iv) the external multiplication of it = (the external multiplication of V )↾[: R, the carrie...
متن کاملSymplectic subspaces of symplectic Grassmannians
Let V be a non-degenerate symplectic space of dimension 2n over the field F and for a natural number l < n denote by Cl(V ) the incidence geometry whose points are the totally isotropic l-dimensional subspaces of V . Two points U, W of Cl (V ) will be collinear when W ⊂ U⊥ and dim(U ∩ W ) = l − 1 and then the line on U and W will consist of all the l-dimensional subspaces of U + W which contain...
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2017
ISSN: 1781-6475,1781-6475
DOI: 10.2140/iig.2017.15.187