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Dual topology of the motion groups
-
Mounir Elloumi
Published/Copyright:
February 8, 2010
Abstract
Let 
, n ⩾ 2, be the classical motion group, where SO(n) acts on 
by rotation. In this paper, we identify the dual space 
, i.e. the set of equivalence classes of irreducible unitary representations of Mn, with the quotient space of admissible co-adjoint orbits 
via a nice geometric parameterization of the two spaces. We show then that this identification is a homeomorphism.
Received: 2008-01-21
Accepted: 2008-05-21
Published Online: 2010-02-08
Published in Print: 2010-March
© de Gruyter 2010
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- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
Articles in the same Issue
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
