共查询到20条相似文献,搜索用时 15 毫秒
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Suppose be a simpleinvolution of a semisimple algebraic group and suppose H is the subgroup of G of pointsfixed by . If the restrictedroot system is of type or and G is simplyconnected, or if the restricted root system is of type and G is of adjoint type, then we describe astandard monomial theory and the equations for the coordinatering using the standardmonomial theory and the Plücker relations of an appropriate(maybe infinite-dimensional) Grassmann variety. 相似文献
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Under consideration are the classes of graphs closed under modulo 2 addition, vertex permutation, and removal of isolated vertices. It is proved that there are exactly five these classes. 相似文献
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Krzysztof Prażmowski 《Journal of Geometry》2001,72(1-2):172-187
In this paper we introduce the notion of spine space, generalizing the notion of affine grassmannians. We describe the set of strong subspaces of a spine space (Thm. 2.6, 2.7), construct the horizon of a spine space, and study the automorphisms of a spine space. Received 20 October 1999; revised 15 March 2000. 相似文献
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E. Mazetis 《Lithuanian Mathematical Journal》1989,29(3):271-276
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We study module spaces for linear relations (multi-valued operators) in a Hilbert space. The defect spaces are not required to be finite-dimensional. In particular we pay attention to module spaces for symmetric relations. 相似文献
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For a given manifold M we consider the non-linear Grassmann manifold Gr
n
(M) of n–dimensional submanifolds in M. A closed (n+2)–form on M gives rise to a closed 2–form on Gr
n
(M). If the original form was integral, the 2–form will be the curvature of a principal S
1
–bundle over Gr
n
(M). Using this S
1
–bundle one obtains central extensions for certain groups of diffeomorphisms of M. We can realize Gr
m–2
(M) as coadjoint orbits of the extended group of exact volume preserving diffeomorphisms and the symplectic Grassmannians SGr
2k
(M) as coadjoint orbits in the group of Hamiltonian diffeomorphisms.
Mathematics Subject Classification (2000):58B20Both authors are supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austrian Science Fund), project number P14195-MAT 相似文献
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Bart De Bruyn 《Linear algebra and its applications》2011,435(5):1055-1084
We investigate relationships between polyvectors of a vector space V, alternating multilinear forms on V, hyperplanes of projective Grassmannians and regular spreads of projective spaces. Suppose V is an n-dimensional vector space over a field F and that An-1,k(F) is the Grassmannian of the (k − 1)-dimensional subspaces of PG(V) (1 ? k ? n − 1). With each hyperplane H of An-1,k(F), we associate an (n − k)-vector of V (i.e., a vector of ∧n−kV) which we will call a representative vector of H. One of the problems which we consider is the isomorphism problem of hyperplanes of An-1,k(F), i.e., how isomorphism of hyperplanes can be recognized in terms of their representative vectors. Special attention is paid here to the case n = 2k and to those isomorphisms which arise from dualities of PG(V). We also prove that with each regular spread of the projective space PG(2k-1,F), there is associated some class of isomorphic hyperplanes of the Grassmannian A2k-1,k(F), and we study some properties of these hyperplanes. The above investigations allow us to obtain a new proof for the classification, up to equivalence, of the trivectors of a 6-dimensional vector space over an arbitrary field F, and to obtain a classification, up to isomorphism, of all hyperplanes of A5,3(F). 相似文献
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In this paper we introduce a special class of finite-dimensional symmetric subspaces of L1, so-called regular symmetric subspaces. Using this notion, we show that for any k?2, there exist k-dimensional symmetric subspaces of L1 which have maximal projection constant among all k-dimensional symmetric spaces. Moreover, L1 is a maximal overspace for these spaces (see Theorems 4.4 and 4.5.) Also a new asymptotic lower bound for projection constants of symmetric spaces is obtained (see Theorem 5.3). This result answers the question posed in [12, p. 36] (see also [15, p. 38]) by H. Koenig and co-authors. The above results are presented both in real and complex cases. 相似文献
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Serguei V. Astashkin 《Journal of Functional Analysis》2005,226(1):173-192
Let X be a rearrangement invariant (r.i.) function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of measurable functions x such that xh∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We show that for a broad class of r.i. spaces X, the space Λ(R,X) is not r.i. In this case, we identify the symmetric kernel of the Rademacher multiplicator space and study when reduces to L∞. In the opposite direction, we find new examples of r.i. spaces for which Λ(R,X) is r.i. We consider in detail the case when X is a Marcinkiewicz or an exponential Orlicz space. 相似文献
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We discuss parabolic contact geometries carrying a smooth system of symmetries. We show that there is a symmetric space such that the parabolic geometry $ \left( {\mathcal{G}\to M,\omega } \right) $ is a fibre bundle over this symmetric space if and only if the base manifold M is a homogeneous reexion space. We investigate the conditions under which there is an invariant geometric structure on this symmetric space induced by the parabolic contact geometry. 相似文献
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W. T. Gowers 《Israel Journal of Mathematics》1989,68(2):193-219
It is shown that for 1 ≦p < ∞, any basisC-equivalent to the unit vector basis ofl
p
n
has a (1 + ε)-symmetric block basis of cardinality proportional ton/logn. When 1 <p < ∞, an upper bound proportional ton log logn/logn is also obtained. These results extend results of Amir and Milman in [2]. 相似文献