Elements of the Representation Theory of the Jacobi GroupCombining algebraic groups and number theory, this volume gathers material from the representation theory of this group for the first time, doing so for both local (Archimedean and non-Archimedean) cases as well as for the global number field case. |
Contents
| 1 | |
2 Basic Representation Theory of the Jacobi Group | 15 |
3 Local Representations The Real Case | 31 |
4 The Space L2GJGJR and its Decomposition | 75 |
5 Local Representations The padic Case | 104 |
6 Spherical Representations | 137 |
7 Global Considerations | 173 |
| 201 | |
| 207 | |
| 211 | |
Other editions - View all
Elements of the Representation Theory of the Jacobi Group Rolf Berndt,Ralf Schmidt Limited preview - 2013 |
Elements of the Representation Theory of the Jacobi Group Rolf Berndt,Ralf Schmidt Limited preview - 1998 |
Elements of the Representation Theory of the Jacobi Group Rolf Berndt,Ralf Schmidt Limited preview - 2012 |
Common terms and phrases
adelic admissible representation Assume automorphic factor automorphic representations classical cocycle compute Corollary corresponding coset cusp condition cuspidal decomposition defined definition denotes differential operators discrete series representation eigenform Eisenstein series element equation equivalent finite first fixed formula Fourier fulfilled functions f given GJ(A GJ(R global H(GJ Hecke algebra Hecke operators Heisenberg group Hence Hilbert space holomorphic identified induced representation infinitesimal integral intertwining invariant isomorphism Jacobi forms Jacobi group Lemma Lie algebra lift lowest weight metaplectic group modular forms non-trivial central character p-adic polynomial positive Weil representation principal series representation Proof Proposition Remark representation 71 representation with X2 representations of GJ resp right translation scalar Schrodinger-Weil representation Schwartz function smooth representation spherical representations spherical vector subspace transformation trivial unique unitary representations unramified Waldspurger Weil representation Whittaker functional Whittaker models