## The Weil representation, Maslov index and Theta seriesThis is a collection of research-oriented monographs, reports, and notes arising from lectures and seminars on the Weil representation, the Maslov index, and the Theta series. It is good contribution to the international scientific community, particularly for researchers and graduate students in the field. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

12 | |

Fourier transforms and intertwining operators | 30 |

Maslov index | 39 |

The cocycle of the ShaleWeil representation | 47 |

Oriented Lagrangian planes and the metaplectic | 64 |

The universal covering group of SL2R | 73 |

The universal covering group of the symplectic | 84 |

A generalization of Maslov index | 104 |

Bibliographical notes | 116 |

Part Thetaseries and applications by Michèle Vergne | 123 |

Bibliographical notes | 330 |

### Other editions - View all

The Weil Representation, Maslov Index and Theta Series Gerard Lion,Michele Vergne No preview available - 2014 |

The Weil Representation, Maslov Index, and Theta Series Gerard Lion,Michèle Vergne No preview available - 1980 |

The Weil representation, Maslov index and Theta series Gerard Lion,Michele Vergne No preview available - 1980 |

### Common terms and phrases

action algebra Ar(Y associated automorphic bilinear form canonical character mod choose cocycle coefficients compute congruence subgroup connected component consider the function corresponding cusp cz+d decomposition denote element equivalent explicit follows form of weight formula given group G harmonic polynomial Heisenberg group Hence Hilbert space holomorphic function identify integral invariant invertible irreducible representation isomorphism kernel Lagrangian subspace Lemma Let us consider Let us write lowest weight vector Maslov index matrix metaplectic group modular forms multiplication obtain orthogonal p(exp positive definite projective representation Proof Proposition prove quadratic form relation representation of SL(2,R respect Rg(g satisfies scalar Section self-dual lattice semi-invariant Shale-Weil representation signature Sp(B symmetric form symplectic basis symplectic group symplectic space symplectic vector space Theorem To(D To(N true representation unitary operator unitary representation universal covering group verify x(exp Zagier