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Showing 1 to 13 of 13 for “"Homogeneous space"”.
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The Grothendieck-Cousin complex on G/B x G/B
… group G. His technique uses the geometry of the homogeneous space G/B, B being a Borel subgroup of G. The complex gives a resolution by B-modules, which easily yields the Weyl character formula.
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The Geodesic Gauss Map and Ruh-Vilms theorem for a Hypersurface in S^{n}
We are interested to work on normal homogeneous space and in this space we calculated Live-Civita connection and we derived a useful equation 2.17. The Ruh-Vilms theorem is a statement about the Gauss map for a submanifold of R^{n+1} . Our aim is to prove, an isometrically immersed hypersurface f : …
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Two problems in the theory of curves over fields of positive characteristic
… Artin-Schreier cover is realized as a principal homogeneous space of Γ. We are especially interested in the case when X is P1\{0,1,∞}, a thrice punctured plane. An argument of (generalized) Artin-Schreier field extension and its function field arithmetic follows. The second half is about the …
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Homomorphisms of semi-holonomic verma modules : an exceptional case.
… part in the theory of invariant operators on homogeneous spaces. If G is a semisimple Lie group and P a parabolic subgroup of G, then there is often a differential geometry for which the homogeneous space G/P represents the flat model. An example is conformal geometry, where G is the special …
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Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves
… ⟨ , ⟩CT on Sel2(J) × Sel2(J) following the homogeneous space definition of the Cassels-Tate pairing. For ε,η ∈ Sel2(J), we compute ⟨ε,η⟩CT both in the case where all points in J[2] are defined over K and in the case where the twisted Kummer surface Kη has a K-rational point. In both cases, …
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Compact Symmetric Spaces, Triangular Factorization, and Cayley Coordinates
… a simply connected, compact Riemannian symmetric space. We can represent X as the homogeneous space U/K, where U is a simply connected compact Lie group, and K is the fixed point set of an involution θ of U. Let G be the complexification of U. We consider the intersections of the image of the …
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BIANCHI-ICOSMOLOGICALMODEL IN f(R,T) GRAVITY
… Amongstthevariousfamiliesofhomogeneous,butanisotropic geometries, the most well-known are the Bianchi type I -IX space-time line elements. However,earlierstudiesonthepossibleeffectsofanisotropicuniversemaketheBianchi type-I model a prime alternative. In particular, a …
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Secant varieties of Spinor varieties and of other generalized Grassmannians
Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Despite they have been studied for decades, several aspects of their geometry are still mysterious, among which identifiability and singularity of their points. In …
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Asymptotics, exact results, and analogies in p-adic random matrix theory
… stochastic processes on the (discrete) homogeneous space GLₙ(Qₚ)/GLₙ(Zₚ) with independent increments. We consider the one with smallest jumps, a p-adic analogue of multiplicative Brownian motion on GLₙ(C)/U(N), and show that the singular numbers of the matrix evolve as independent …
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Homogeneous spaces with the cohomology of sphere products and compact quadrangles
We consider homogeneous spaces G/H with the same rational homotopy as a product of a 1-sphere and a (m+1)-sphere. We show that these spaces have also the rational cohomology of such a sphere product if H is connected and if the quotient has dimension m+2. Furthermore, we prove that if additionally …
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Lorentzian Poisson homogeneous spaces, quantum groups and noncommutative spacetimes
El objetivo de esta Tesis Doctoral es el estudio de ciertas deformaciones cuánticas de los grupos cinemáticos Lorentzianos (Poincaré y (anti-)de Sitter), sus espacios homogéneos cuánticos asociados, y algunas de sus consecuencias físicas. En particular, se construye el espacio no conmutativo de …
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Topological effects in particle physics phenomenology
… maps from an arbitrary worldvolume manifold to a homogeneous space $G/H$ (where $G$ is an arbitrary Lie group and $H \subset G$). Such models are ubiquitous in phenomenology; in three or more dimensions they cover all cases in which only some subgroup $H$ of a dynamical symmetry group $G$ is …
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On Gaussian multiplicative chaos and conformal field theory
… worldsheet, i.e. an embedding of a surface into space-time. The path integral that Polyakov wrote down features a random conformal factor that should be described by the quantisation of the Liouville action. Therefore, this probability measure should describe random fluctuations around the …