Elements of the Representation Theory of the Jacobi Group
- PDF / 16,005,933 Bytes
- 226 Pages / 439.37 x 666.142 pts Page_size
- 16 Downloads / 243 Views
Series Editors H. Bass
J. Oesterle A. Weinstein
RoIfBemdt Ralf Schmidt
Elements of the Representation Theory oftheJacobiGroup
Springer Basel AG
Authors: Rolf Berndt and Ralf Schmidt Mathematisches Seminar der Universität Harnburg Bundesstr. 55 D-20146 Harnburg Germany 1991 Mathematics Subject C1assification 11FXX, 14K25
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data Berndt, Rolf: Elements of the representation theory of the Jacobi Group I Rolf Berndt ; Ralf Schmidt. - Basel ; Boston ; Berlin : Birkhäuser, 1998 (Progress in mathematics; Vol. 163) ISBN 978-3-7643-5922-5 ISBN 978-3-0348-8772-4 (eBook) DOI 10.1007/978-3-0348-8772-4
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind ofuse whatsoever, permission from the copyright owner must be obtained.
© 1998 Springer Basel AG Softcoverreprint of the hardcover 1st edition 1998 Originally published by Birkhäuser Verlag Printed on acid-free paper produced of chlorine-free pulp. TCF
Auffallender Weise hat eine so wiehtige Function noeh keinen andern Namen, ais den der Transeendente e, naeh der zufi:illigen Bezeiehnung, mit der sie zuerst bei J a e 0 b i erseheint, und die Mathematiker wiirden nur eine PRieht der Dankbarkeit erfiillen, wenn sie sieh vereinigten ihr J a e 0 b i s Namen beizuiegen, urn das Andenken des Mannes zu ehren, zu dessen sehonsten Entdeekungen es gehort, die innere Natur und hohe Bedeutung dieser Transeendente zuerst erkannt zu haben. from: L. DIRICHLET: Gediiehtnisrede auf C.G .J . JACOBI
Preface
The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. Its importance prima facie stems from the fact that it sets the frame to treat theta functions and elliptic and abelian functions . Up to now, most work concerning this group has been done for the simplest case "of degree one" , where the symplectic group is simply 8L(2) and the Heisenberg group is a three parameter nilpotent group. The Jacobi group, whose theory is intensively interwoven with that of the metaplectic group, is, together with the Heisenberg group, the most evident example for a non-reductive group. This treatise is meant to show how the general theory of automorphic forms for reductive groups extends by some slight alterations to this first more general example. The reader will see that a lot of the following may easily be extended to the higher degree case of a semidirect product of a symplectic group 8p(n) with a corresponding Heisenberg group. We were tempted to do this, but as the generalizations are sometimes fairly easy on the one hand, and as the degreeone case has special features, e.g. concerning the cusp conditions, on the other hand, we restrict ourselves to this case, denoted GJ, here.
Co
Data Loading...
