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Showing 1 to 17 of 17 for “"SYMMETRIC SPACES"”.
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Symmetric spaces
… review the basic theory of a general class of symmetric spaces with canonical reflections, midpoints, and displacement groups. We introduce a notion of gyrogroups established by A. A. Ungar and define gyrovector spaces slightly different from Ungar's setting. We see the categorical equivalence …
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Immersions of symmetric spaces,
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1970.
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Character sheaves on symmetric spaces
… we apply the theory of character sheaves on a symmetric space (h la Ginzburg and Grojnowski) to the problem of determining the spherical functions (averages of the irreducible characters) of the associated symmetric space over a finite field. A crucial result about the filtration of character …
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Character sheaves on symmetric spaces
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1992
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Compact Symmetric Spaces, Triangular Factorization, and Cayley Coordinates
Let X be 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 …
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Vector valued Poisson transforms on Riemannian symmetric spaces
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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The Segal-Bargmann transform on inductive limits of compact symmetric spaces
… transform on the direct limit of the Hilbert spaces $\{L^2(M_n)^{K_n}\}_n$ where $\{M_n = U_n/K_n\}_n$ is a propagating sequence of symmetric spaces of compact type with the assumption that $U_n$ is simply connected for each $n$. This map is obtained by taking the direct limit of the …
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Isometries on symmetric spaces associated with semi-finite von Neumann algebras
Isometries on Banach spaces of measurable functions can typically be characterized as weighted composition operators. In the non-commutative setting, isometries between symmetric spaces (of trace-measurable operators) can often be described in terms of a Jordan ✽-homomorphism (which may be …
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On Multi-component Nonlinear Schrödinger Equation with PT-Symmetry
… with parity- time (PT)-symmetry related to symmetric spaces. This includes: the spectral properties of the associated Lax operator, Jost solution, the scattering matrix, the minimal sets of scattering data and the fundamental analytic solutions. We also derive the completeness relations of …
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On the Isomorphy Classes of Involutions over SO(2n, k)
… of Dr. Aloysius Helminck). 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 …
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Witt groups of complex varieties
… applies in particular to projective homogeneous spaces. By extending known computations in topology, we obtain an additive description of the Witt groups of all projective homogeneous varieties that fall within the class of hermitian symmetric spaces.
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Partial Cosine-Funk Transforms at Poles of the Cosine-λ Transform on Grassmann Manifolds
… the Grassmannian manifolds of p-dimensional subspaces in K<sup>n</sup> where K is R, C or the skew field H of quaternions. We treat the Grassmannians as the symmetric spaces SO(n)/S(O(p) × O(q)), SU(n)/S(U(p) × U(q)) and Sp(n)/(Sp(p) × Sp(q)) and we work by analogy with the case of the cosine-λ …
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Linear Algebra, Random Matrices and Lie Theory
… the link between classical random matrices and symmetric spaces by introducing this generalized approach. Furthermore, two new families of the Jacobi ensemble parameters are obtained as a result.
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Invariant Frechet algebras on bounded symmetric domains
… the complex vector space Cn . We say that D is symmetric iff, given any two points p, q ∈ D, there is a biholomorphism &phis;, which interchanges p and q. These domains were classified abstractly by Elie Cartan in his general study of symmetric spaces, and were canonically realized in Cn by …
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Point processes of representation theoretic origin
… representations of certain infinite-dimensional symmetric spaces. In representation-theoretic terms, our result solves the problem of noncommutative harmonic for the aforementioned family of representations. The second part of the text is based on joint work with Grigori Olshanski. We consider a …
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Aspects of higher degree forms with symmetries
… of Harrison's treatment of higher degree symmetric forms. We explain antisymmetrization; discuss the derivative of an alternating form and its corresponding anticommutative polynomial; define alternating spaces and their direct sum; establish decomposition and cancellation results for …
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Wordline approach to higher spin fields
… in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for …