Another proof for the continuity of the Lipsman mapping
DOI:
https://doi.org/10.37863/umzh.v72i7.548Keywords:
Lie groups, semidirect product, unitary representations, coadjoint orbits, symplectic inductionAbstract
UDC 515.1
We consider the semidirect product G=K⋉V where K is a connected compact Lie group acting by automorphisms on a finite dimensional real vector space V equipped with an inner product ⟨,⟩. By ˆG we denote the unitary dual of G and by g‡/G the space of admissible coadjoint orbits, where g is the Lie algebra of G. It was pointed out by Lipsman that the correspondence between ˆG and g‡/G is bijective. Under some assumption on G, we give another proof for the continuity of the orbit mapping (Lipsman mapping)
Θ:g‡/G−→ˆG.
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