### 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 |
---|---|

Pages (from-to) | 237-253 |

Number of pages | 17 |

Journal | Monatshefte fur Mathematik |

Volume | 128 |

Issue number | 3 |

Publication status | Published - 1999 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*128*(3), 237-253.

**The contraction of S2p-1 to Hp-1
.** / Dooley, A. H.; Gupta, S. K.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 128, no. 3, pp. 237-253.

}

TY - JOUR

T1 - The contraction of S2p-1 to Hp-1

AU - Dooley, A. H.

AU - Gupta, S. K.

PY - 1999

Y1 - 1999

N2 - A contraction of the sphere S2p 1, considered as the homogeneous space U(p)/U(p - 1), to the Heisenherg group Hp-1 is defined. The infinite dimensional irreducible unitary representations of Heisenberg group Hp-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.

AB - A contraction of the sphere S2p 1, considered as the homogeneous space U(p)/U(p - 1), to the Heisenherg group Hp-1 is defined. The infinite dimensional irreducible unitary representations of Heisenberg group Hp-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.

KW - Contraction

KW - Heisenberg group

KW - Matrix coefficients

KW - Sphere

KW - Unitary groups

UR - http://www.scopus.com/inward/record.url?scp=0012897430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012897430&partnerID=8YFLogxK

M3 - Article

VL - 128

SP - 237

EP - 253

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 3

ER -