### Abstract

By using trace formulae, the recent concept of upper multiplicity for an irreducible representation of a C*-algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent Lie group G. In particular, it is shown that if pi is an element of (G) over cap has finite upper multiplicity then this integer is the greatest strength with which a sequence in (G) over cap can converge to pi. Upper multiplicities are calculated for all irreducible representations of the groups in the threadlike generalization of the Heisenberg group. The values are computed by combining new C-*-theoretic results with detailed analysis of the convergence of coadjoint orbits and they show that every positive integer occurs for this class of groups. (C) 2001 Academic Press.

Original language | English |
---|---|

Pages (from-to) | 26-65 |

Number of pages | 39 |

Journal | Advances in Mathematics |

Volume | 158 |

DOIs | |

Publication status | Published - Mar 2001 |

### Keywords

- IRREDUCIBLE REPRESENTATIONS
- LOWER MULTIPLICITY
- BOUNDED TRACE

### Cite this

*Advances in Mathematics*,

*158*, 26-65. https://doi.org/10.1006/aima.2000.1960

**Strength of convergence in Duals of C*-Algebras and Nilpotent Lie Groups.** / Archbold, Robert J; Kaniuth, E.; Ludwig, J.; Schlichting, G.; Somerset, Douglas W B.

Research output: Contribution to journal › Article

*Advances in Mathematics*, vol. 158, pp. 26-65. https://doi.org/10.1006/aima.2000.1960

}

TY - JOUR

T1 - Strength of convergence in Duals of C*-Algebras and Nilpotent Lie Groups

AU - Archbold, Robert J

AU - Kaniuth, E.

AU - Ludwig, J.

AU - Schlichting, G.

AU - Somerset, Douglas W B

PY - 2001/3

Y1 - 2001/3

N2 - By using trace formulae, the recent concept of upper multiplicity for an irreducible representation of a C*-algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent Lie group G. In particular, it is shown that if pi is an element of (G) over cap has finite upper multiplicity then this integer is the greatest strength with which a sequence in (G) over cap can converge to pi. Upper multiplicities are calculated for all irreducible representations of the groups in the threadlike generalization of the Heisenberg group. The values are computed by combining new C-*-theoretic results with detailed analysis of the convergence of coadjoint orbits and they show that every positive integer occurs for this class of groups. (C) 2001 Academic Press.

AB - By using trace formulae, the recent concept of upper multiplicity for an irreducible representation of a C*-algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent Lie group G. In particular, it is shown that if pi is an element of (G) over cap has finite upper multiplicity then this integer is the greatest strength with which a sequence in (G) over cap can converge to pi. Upper multiplicities are calculated for all irreducible representations of the groups in the threadlike generalization of the Heisenberg group. The values are computed by combining new C-*-theoretic results with detailed analysis of the convergence of coadjoint orbits and they show that every positive integer occurs for this class of groups. (C) 2001 Academic Press.

KW - IRREDUCIBLE REPRESENTATIONS

KW - LOWER MULTIPLICITY

KW - BOUNDED TRACE

U2 - 10.1006/aima.2000.1960

DO - 10.1006/aima.2000.1960

M3 - Article

VL - 158

SP - 26

EP - 65

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -