Search results for " canonical forms"

showing 5 items of 5 documents

L'azione del gruppo simplettico associata ad un'estensione quadratica di campi

2000

Given a quadratic extension L/K of fields and a regular alternating space (V; f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group Sp_L(V; f) in the set of K-subspaces of V.

Geometry of classical groups canonical forms reduction classificationSettore MAT/03 - Geometria
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Unitary Groups Acting on Grassmannians Associated with a Quadratic Extension of Fields

2006

Let (V, H) be an anisotropic Hermitian space of finite dimension over the algebraic closure of a real closed field K. We determine the orbits of the group of isometries of (V, H) in the set of K-subspaces of V . Throughout the paper K denotes a real closed field and K its algebraic closure. Then it is well known (see, for example, [4, Chapter 2], [23]; see also [8]) that K = K(i) with i = √−1. Also we let (V,H) be an anisotropic Hermitian space (with respect to the involution underlying the quadratic field extension K/K) of finite dimension n over K. In this context we consider the natural action of the unitary group U = U(V,H) of isometries of (V,H) on the set Xd of all ddimensional K-subs…

Discrete mathematicsClassical groupPure mathematicsDouble cosetProjective unitary groupGeneral Mathematics15A21Unitary matrixSettore MAT/04 - Matematiche ComplementariAlgebraic closure11E39Unitary group51N30Quadratic fieldGeometry of classical groups Canonical forms reductions classificationSpecial unitary groupMathematicsRocky Mountain Journal of Mathematics
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The Action of the Symplectic Group Associated with a Quadratic Extension of Fields

1999

Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.

Discrete mathematicsPure mathematicsSymplectic groupAlgebra and Number TheoryGroup (mathematics)Symplectic representationSymplectic vector spaceQuadratic equationDimension (vector space)Metaplectic groupSettore MAT/03 - GeometriaMoment mapMathematicsGeometry of classical groups Canonical forms reduction classificationJournal of Algebra
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The action of the unitary group associated with a quadratic extension of fields

1999

Given a quadratic extension L/k of fields of characteristic different from 2 and a unitary space (V, f) of finite dimension over L, we give a representation, as simple as possible, of the form which f induces by restriction on a k-substructure of V. This, in turn, allows one to study the orbits of the unitary group U(V, f) in the set of k-substructures of V of a given dimension.

Settore MAT/03 - GeometriaGeometry of classical groups Canonical forms reduction classification
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Unitary groups acting on hyperbolic substructures

2005

Given a quadratic extension L/K of fields and a regular l-Hermitian space (V,h) of finite dimension over L, we study the orbits of the group of isometries of (V,h) in the set of hyperbolic K-substructures of V.

Geometry of classical groups canonical forms reductions classification.Settore MAT/04 - Matematiche Complementari
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