The Weil Representation, Maslov Index and Theta Series: 006 (Progress in Mathematics)

\* A collection of research-oriented monographs, reports, notes arising from lectures or seminars \* Quickly published concurrent with research \* Easily accessible through international distribution facilities \* Reasonably priced \* Reporting research developments combining original results with an expository treatment of the particular subject area \* A contribution to the international scientific community: for colleagues and for graduate students who are seeking current information and directions in their graduate and post-graduate work Front Matter....Pages i-viii Front Matter....Pages 1-1 Introduction....Pages 3-6 Symplectic vector spaces and the Heisenberg Lie algebra....Pages 7-11 The Heisenberg group and the Schrödinger representation....Pages 12-15 The Weyl transform and the Stone-Von Neumann theorem....Pages 16-29 Fourier transforms and intertwining operators....Pages 30-38 Maslov index....Pages 39-46 The cocycle of the Shale-Weil representation and the Maslov index....Pages 47-63 Oriented Lagrangian planes and the metaplectic group....Pages 64-72 The universal covering group of SL(2,R)....Pages 73-83 The universal covering group of the symplectic group....Pages 84-103 Front Matter....Pages 121-121 Introduction....Pages 123-137 Lattices and representations of the Heisenberg group....Pages 138-148 The multiplier of θ....Pages 149-176 Modular forms on the upper half-plane....Pages 177-196 Modular forms of weight 1/2....Pages 197-208 The Shale-Weil representation associated to a quadratic form....Pages 209-246 θ-Series Associated to Quadratic forms....Pages 247-267 The Shimura correspondence....Pages 268-285 Zagier modular forms and the Doi-Naganuma correspondence....Pages 286-309 Cohen lifting of modular forms....Pages 310-329 This 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. Gérard Lion, Michèle Vergne. Includes Bibliographical References.