### Abstract

A contraction of the sphere S^{2p 1}, considered as the homogeneous space U(p)/U(p - 1), to the Heisenherg group H^{p-1} is defined. The infinite dimensional irreducible unitary representations of Heisenberg group H^{p-1} are then shown to be the limits of the irreducible representations of U(p) which are class-1 with respect to U(p - 1). Our results generalise the earlier results of Fulvio Ricci.

Original language | English |
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Pages (from-to) | 237-253 |

Number of pages | 17 |

Journal | Monatshefte fur Mathematik |

Volume | 128 |

Issue number | 3 |

Publication status | Published - 1999 |

### Keywords

- Contraction
- Heisenberg group
- Matrix coefficients
- Sphere
- Unitary groups

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Dooley, A. H., & Gupta, S. K. (1999). The contraction of S2p-1 to Hp-1
.

*Monatshefte fur Mathematik*,*128*(3), 237-253.