Compact Lie Groups
Mostrando 1-12 de 14 artigos, teses e dissertações.
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1. Planejamento periódico de trajetórias de sistemas afins sem arrasto em grupos de Lie compactos / Periodic motion planning of trajectories for control-affine driftless systems in compact Lie groups
We treat the periodic motion planning problem: given a periodic trajectory of a control-affine driftless system in a compact and connected Lie group G and an initial condition in G, find another trajectory of the same system satisfying the initial condition given and that asymptotically tracks the periodic trajectory. We solve this problem locally (for initi
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia. Publicado em: 08/03/2012
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2. Grupos de Lie compactos / Compact Lie groups
Neste trabalho apresentamos os principais resultados da teoria dos grupos de Lie compactos e provamos o Teorema de Weyl sobre os seus grupos fundamentais.
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia. Publicado em: 20/04/2011
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3. Algebraic methods for the computation of general reversible-equivariant mappings / Métodos algébricos para a obtenção de formas gerais reversíveis-equivariantes
In the global and local analysis of dynamical systems, we assume, in general, that the equations are in a normal form. In presence of symmetries, the equations and the problem domain are invariant under the group formed by these symmetries; in that case, the vector field is equivariant by the action of this group. When, in addition to the symmetries, we have
Publicado em: 2009
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4. O Teorama da Convexidade do Mapa do Momento
In this dissertation we presented the Atiyah-Guillemin-Sternberg convexity theorem about the image of the moment map in the case of Hamiltonian torus action on compact connected symplectic manifold. This result gives, in certain sense, a generalization to Schur theorem about relationship between eigenvalues and diagonal entries of Hermitian matrix. With this
Publicado em: 2007
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5. Estruturas quase hermitianas invariantes e ideais abelianos
Let G be a complex semi-simple Lie group and form its maximal flag manifold F = G/P = U/T where P is a minimal parabolic subgroup, U a compact real form and T = U P a maximal torus of U. We study U -invariant almost Hermitian structures on F. The (1, 2)-symplectic (or quasi-Kähler) structures are naturally related to the affine Weyl groups. A special form f
Publicado em: 2003
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6. Coherent states: the symplectic goup and generalizations / Estados coerentes: o grupo simplético e generalizações.
The subject of the Thesis was the aplication of the coherent states theory to non-trivial quantum systems. Starting from the general definition of coherent states for compact Lie groups, we made a detailed investigation of the construction of these states and its properties in the case of the unitary symplectic group Sp(4), which is extremely important in bo
Publicado em: 2003
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7. Signature quantization and representations of compact Lie groups
We discuss some applications of signature quantization to the representation theory of compact Lie groups. In particular, we prove signature analogues of the Kostant formula for weight multiplicities and the Steinberg formula for tensor product multiplicities. Using symmetric functions, we also find, for type A, analogues of the Weyl branching rule and the G
National Academy of Sciences.
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8. Multipliers on Compact Lie Groups
Sufficient conditions are found for a biinvariant operator on a compact Lie group to be bounded on Lp, 1 < p < ∞. The proof uses properties of g-functions on such a group, and an analog to the familiar relationship between differentiation and multiplication under the Fourier transform.
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9. Dedekind's η-function and the cohomology of infinite dimensional Lie algebras
We compute the cohomology of certain infinite dimensional Lie algebras which are subalgebras of Lie algebras introduced by Moody and Kac. We note a relation between our results and the cohomology of loop spaces of compact groups. Finally, we derive, by Euler-Poincaré, identities of Macdonald for powers of the Dedekind η-function.
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10. Differentiable Cohomology on Locally Compact Groups
In this paper the notions of vector field and differential form are extended to locally compact groups which are the inverse limit of Lie groups. This is done using Bruhat's definition of [unk]c∞ functions on such a group. Vector fields are defined as derivations on the [unk]c∞ functions. Then tangent vectors at a point are defined as elements of the inv
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11. THE PLANCHEREL FORMULA FOR SL(2) OVER A LOCAL FIELD*
More than two decades ago, in his classical paper on the irreducible unitary representations of the Lorentz group, V. Bargmann initiated the concrete study of Fourier analysis on real Lie groups and obtained the analogue of the classical Fourier expansion theorem in the case of the Lorentz group. Since then the general theory for real semisimple Lie groups h
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12. Classification of the irreducible representations of semisimple Lie groups
We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G, in terms of their restriction to a maximal compact subgroup K of G. (A classification in terms of analytic properties of the representations has been given by R. P. Langlands [(1973), mimeographed notes, Institute for Advanced Study, Princeton, N