The Weil representation, Maslov index and Theta series

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