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Showing 1 to 10 of 10 for “"orthogonal group"”.
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Modular forms for the orthogonal group O(2,5)
This thesis deals with modular forms for orthogonal groups of signature (2,n), n>2, with particular emphasis on the case n=5. First we determine suitable generators and the abelian characters of some orthogonal groups. Then we present a few methods for constructing orthogonal modular forms: by …
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The ring of invariants of the orthogonal group over finite fields in odd characteristic
… of the dual of V we are concerned with the Orthogonal group $O(\xi_0)$, the subgroup of the General Linear Group $GL(V)$ that fixes $\xi_0$ and with invariants of this group. We have the Dickson Invariants which being invariants of the General Linear Group are then invariants of $O(\xi_0)$. …
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Homomorphisms of semi-holonomic verma modules : an exceptional case.
… 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 orthogonal group SO(n, C). A Verma module …
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Constrained Optimization on SO(3), via Pseudospectral Collocation
… relatively few collocation points. The special orthogonal group, SO(3), is both a Lie group and a manifold, and thus demands on-manifold optimization techniques to preserve its geometric structure. Riemannian optimization is enabled by mapping problems to the tangent space through equivariant …
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On the Isomorphy Classes of Involutions over SO(2n, k)
… The study of symmetric spaces involves group theory, ï¬ eld theory, linear algebra, and Lie algebras, as well as involving the related disciplines of topology, manifold theory, and analysis. The notion of symmetric space was generalized in the 1980’s to groups deï¬ ned over arbitrary …
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Die Struktur rotationsinvarianter Paley-Wiener-Räume : mit einer Anwendung auf Abtastprobleme
… are invariant under the action of the special orthogonal group. The main tool in this connection is the Fourier-Laplace expansion. The rotation invariant Paley-Wiener spaces are completely characterized in terms of the so called radial Fourier-Laplace coefficients. In this context we in …
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Rigid Body Constrained Motion Optimization and Control on Lie Groups and Their Tangent Bundles
… motion are accounted for appropriately. Two Lie groups, the special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual …
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Manifold Optimization for Robotic Perception
… reside in the manifold space, i.e., the special orthogonal group SO(3), where Euclidean geometry with which we are familiar is no longer applicable. To reliably and accurately deploy state estimation algorithms for realworld applications, the underlying optimization problems must be able to …
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Invariant polynomials and machine learning
… of Weyl which tell us that the algebra of orthogonal group-invariant polynomials in $n$ $d$-dimensional vectors is generated by the dot products and that the redundancies which arise when $n > d$ are generated by the $(d+1)$-minors of the $n \times n$ matrix of dot products. We prove the …
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Automorphism groups of self-dual codes
… information. The dual of such a code is the orthogonal space with respect to a Euclidian or Hermitian scalar product. A code which equals its dual is called self-dual. Self-dual codes are of particular interest, for instance since invariant theory provides an overview of the possible weight …