On the universal covering group of the real symplectic group
نویسندگان
چکیده
منابع مشابه
Least-Squares on the Real Symplectic Group
The present paper discusses the problem of least-squares over the real symplectic group of matrices Sp(2n,R). The least-squares problem may be extended from flat spaces to curved spaces by the notion of geodesic distance. The resulting non-linear minimization problem on manifold may be tackled by means of a gradient-descent algorithm tailored to the geometry of the space at hand. In turn, gradi...
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In this paper, we study the restrictions of the complementary series representation onto a symplectic subgroup no bigger than half of the size of the original symplectic group.
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Let S̃p(n,R) be the universal covering of the symplectic group. In this paper, we study the restrictions of the degenerate unitary principal series I( , t) of S̃p(n,R) onto S̃p(p,R)S̃p(n − p,R). We prove that if n ≥ 2p , I( , t)| S̃p(p,R)S̃p(n−p,R) is unitarily equivalent to an L 2 -space of sections of a homogeneous line bundle L(S̃p(n − p,R) × G̃L(n−2p)N C ,t+ρ) (see Theorem 1.1). We further study th...
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Let S̃p(q,R) be the universal covering of the symplectic group. In this paper, we study the unitarity problem for the representation induced from a one dimensional character ( , v) of G̃L(q − p) tensoring with a unitary representation σ0 of a smaller S̃p(p,R). We establish the unitarity when the real character v is in a certain interval depending on and σ0 satisfies a certain growth condition. We ...
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In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2012
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2012.05.009