A decomposition of the natural embedding spaces for the symplectic dual polar spaces
نویسندگان
چکیده
منابع مشابه
On isometric full embeddings of symplectic dual polar spaces into Hermitian dual polar spaces
Let n ≥ 2, let K,K′ be fields such that K′ is a quadratic Galoisextension of K and let θ denote the unique nontrivial element in Gal(K′/K). Suppose the symplectic dual polar space DW (2n− 1,K) is fully and isometrically embedded into the Hermitian dual polar space DH(2n − 1,K′, θ). We prove that the projective embedding of DW (2n − 1,K) induced by the Grassmann-embedding of DH(2n − 1,K′, θ) is ...
متن کاملLocally subquadrangular hyperplanes in symplectic and Hermitian dual polar spaces
In [11] all locally subquadrangular hyperplanes of finite symplectic and Hermitian dual polar spaces were determined with the aid of counting arguments and divisibility properties of integers. In the present note we extend this classification to the infinite case. We prove that symplectic dual polar spaces and certain Hermitian dual polar spaces cannot have locally subquadrangular hyperplanes i...
متن کاملOn a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces
Let ∆ be a symplectic dual polar space DW (2n−1, K) or a Hermitian dual polar space DH(2n − 1, K, θ), n ≥ 2. We define a class of hyperplanes of ∆ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space DH(2n−1, K, θ) arising from its Grassmann-...
متن کاملOn the Decomposition of Hilbert Spaces
Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...
متن کاملPolar Decomposition for P-adic Symmetric Spaces
Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.05.023