The contraction of \(S^{2p-1}\) to \(H^{p-1}\)
Let \(G = SU(p,1),G = KAN\) its Iwasawa decomposition, \(K = S(U(p)\times U(1))\), also \(G = PN\), its Levi decomposition, let \(\overline{N}\) be the opposite of \(N\). For \(\varepsilon > 0\), there is defined an open map \(\pi_{\varepsilon} : \overline{N}M\to K\), its domain is relatively compact and its image is dense in \(K\) and \(\pi_{1}\) is a diffeomorphism (Theorem 2.1). In Section 3, certain Fock representations of \(\overline{N}\), which is isomorphic to the Heisenberg group \(H^{p}\), are constructed and an orthonormal basis is given. In Section 4, M class-1 representations of \(K\) are constructed, where \(P = MA\). In Section 5, the main theorem, which describes the approximation of the matrix coefficients of \(\overline{N}\) by those of an \(M\) class-1 representation of \(K\), is given (Theorem 5.1).
scientific article; zbMATH DE number 1382946