Heisenberg motion groups and their cortex

Aymen Rahali ()
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Aymen Rahali: Université de Sfax, Faculté des Sciences Sfax

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 570-577

Abstract: Abstract Let $$G_n:=U(n)\ltimes {\mathbb {H}}_n$$ G n : = U ( n ) ⋉ H n be the semidirect product of the unitary group acting by automorphisms on the Heisenberg group $${\mathbb {H}}_n.$$ H n . It was pointed out in [5], that the unitary dual $$\widehat{G_n}$$ G n ^ of $$G_n$$ G n is homeomorphic to the space of admissible coadjoint orbits $${\mathfrak {g}}_n^\ddagger /G_n$$ g n ‡ / G n of $$G_n.$$ G n . One of the important subset of $$\widehat{G_n}$$ G n ^ is what is called the cortex of $$G_n,$$ G n , cor $$(G_n),$$ ( G n ) , which is the set of all $$\pi \in \widehat{G_n}$$ π ∈ G n ^ that cannot be Hausdorff separated from the identity representation $$1_{G_n}$$ 1 G n of $$G_n.$$ G n . In the present paper, we use the orbit method of Lipsman to determine the cortex of $$G_n.$$ G n .

Keywords: Lie groups; Semidirect product; Unitary representations; Coadjoint orbits; Cortex of locally compact groups; 22D10-22E27-22E45 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00134-4

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