## Abstract

We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family script G sign → B of Lie groups (these families are called "gauge-invariant families" in what follows). If the fibers of G → B are simply-connected and solvable, we compute the Chern character of the gauge-equivariant index, the result being given by an Atiyah-Singer type formula that incorporates also topological information on the bundle script G sign → B. The algebras of invariant pseudodifferential operators that we study, ψ_{inv}^{∞}(Y) and Ψ_{inv}^{∞}(Y), are generalizations of "parameter dependent" algebras of pseudodifferential operators (with parameter in R^{q}). so our results provide also an index theorem for elliptic, parameter dependent pseudodifferential operators. We apply these results to study Fredholm boundary conditions on a simplex.

Original language | English (US) |
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Pages (from-to) | 155-183 |

Number of pages | 29 |

Journal | Acta Mathematica Hungarica |

Volume | 99 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 2003 |

## All Science Journal Classification (ASJC) codes

- General Mathematics