We consider a 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 Ĝ we denote the unitary dual of G and by 𝔤‡/G we denote the space of admissible coadjoint orbits, where 𝔤 is the Lie algebra of G. It was indicated by Lipsman that the correspondence between Ĝ and 𝔤‡/G is bijective. Under certain assumptions on G, we give another proof of continuity for the orbit mapping (Lipsman mapping)
Θ : 𝔤‡/ G → Ĝ.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 7, pp. 945–951, July, 2020. Ukrainian DOI: 10.37863/umzh.v72i7.548.
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Messaoud, A., Rahali, A. Another Proof for the Continuity of the Lipsman Mapping. Ukr Math J 72, 1100–1107 (2020). https://doi.org/10.1007/s11253-020-01845-3
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DOI: https://doi.org/10.1007/s11253-020-01845-3