May 19, 1998 · "The book under review collects and regroups results on the representation theory of the Jacobi group of lowest degree mostly due to R.Berndt and his coworkers J.Homrighausen and R.Schmidt. The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. Elements of the Representation Theory of the Jacobi Group. Authors: Berndt, Rolf, Schmidt, Ralf. Free Preview. Very well written monograph combining algebraic groups and number theory. Recommended reading for researchers of modular and automorphic forms. Up to date and structured collection of known results. The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local archimedean and.
Elements of the Representation Theory of the Jacobi Group Rolf Berndt, Ralf Schmidt auth. download B–OK. Download books for free. Find books. Elements of the representation theory of the Jacobi group. [Rolf Berndt; Ralf Schmidt] -- The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions.
ISBN: 0817659226 9780817659226 3764359226 9783764359225: OCLC Number: 38910274: Description: xiii, 213 pages; 24 cm. Contents: 1. The Jacobi Group --2.Basic Representation Theory of the Jacobi Group --3.Local Representations: The Real Case --4.The Space L[superscript 2]T[superscript J]\G[superscript J]R and its Decomposition --5.Local Representations: The p-adic. Berndt R., Schmidt R. 1998 Basic Representation Theory of the Jacobi Group. In: Elements of the Representation Theory of the Jacobi Group. Progress in Mathematics, vol 163.
The Jacobi group is a semidirect product of a semisimple symplectic group with a nilpotent Heisenberg group. It comes along in several presentations which may be more or less appropriate for the different parts of the theory. So we will discuss here several realizations and change from one to the other from time to time. Joint with Rolf Berndt: Elements of the Representation Theory of the Jacobi Group. Birkhäuser, Progress in Mathematics 163, Boston 1998; Spherical representations of the Jacobi group. Abh. Math. Sem. Univ. Hamburg 68 1998, 273-296; On old and new Jacobi forms. J. Number Theory 79 1999, 29-57; Joint with Rolf Berndt: Local Maaß lifts. Rolf Berndt and Ralf Schmidt, Elements of the representation theory of the Jacobi group, Progress in Mathematics, vol. 163, Birkhäuser Verlag, Basel, 1998. MR 1634977 [B-Z] I. N. Bernstein and A. V. Zelevinsky, Induced representations of reductive 픭-adic groups. tions of the Jacobi group attached to Jacobi forms of square free index. We are assuming some familiarity with the representation theory of the Jacobi group, in particular the classification of local representations. A detailed account is given in . Incidentally. The squeezed states for the unitary irreducible representation of the Jacobi group are introduced. R. Schmidt, Elements of the repr esentation theory of the. Jacobi gr oup, Progress in.
There are already many good books on representation theory for all kinds of groups. Two of the best in this author’s opinion are the one by A.W. Knapp: “Representation Theory for Semisimple Groups. An Overview based on Examples” [Kn1] and by G.W. Mackey: “Induced Representations in Physics, Probability and Number Theory” [Ma1]. the Jacobi Theory1 Ralf Schmidt Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395 Communicated by S. Rallis Received June 10, 1999 The study of spherical representations of the Jacobi group begun in R. Schmidt, 1998, Abh. Math. Sem. Univ. Hamburg 68, 273 296 is continued. Using certain. This section provides the lecture notes from the course. The present lecture notes arose from a representation theory course given by Prof. Etingof in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students. The students in that course — Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Elena Yudovina, and Dmitry Vaintrob — co. Advancing research. Creating connections. ISSN 1088-6826online ISSN 0002-9939print.
Nov 01, 1999 · Certain “index shifting operators” for local and global representations of the Jacobi group are introduced. They turn out to be the representation theoretic analogues of the Hecke operators U d and V d on classical Jacobi forms, which underlie the theory of Jacobi old- and newforms. Further analogues of these operators on spaces of classical elliptic cusp forms are also investigated. Elements of the Representation Theory of the Jacobi Group PM 163 Birkhäuser Basel 1998 joint work with Ralf Schmidt Erich Kähler. Mathematische Werke/Mathematical Works Walter de Gruyter Berlin 2003 joint edition with Oswald Riemenschneider Representations of Linear Groups An Introduction Based on Examples from Physics and Number Theory.
In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form. Elements Of The Theory Of Computation also available for Read Online in Mobile and Kindle. Elements of the Representation Theory of the Jacobi Group. Author: Rolf Berndt,Ralf. Assuming only a basic understanding of general computer programming and discrete mathematics, Theory of Computation serves as a valuable book for courses on theory. The treatment is self-contained, and makes no special demand on the reader's knowledge beyond the elements of complex analysis in one variable, and of group theory. Elements of the Representation Theory of the Jacobi Group.
R. Berndt, R. Schmidt, Elements of the representation theory of the Jacobi group, Progress in Mathematics, 163. Birkhuser Verlag, Basel, 1998. [Boe] Homomorphisms between generalized Verma. Berndt, Rolf; Ralf Schmidt 1998. 《Elements of the representation theory of the Jacobi group》. Progress in Mathematics 영어 163. Birkhäuser Verlag. doi: 10.1007/978-3-0348-0283-3. The goal of this course is to give an undergraduate-level introduction to representation theory of groups, Lie algebras, and associative algebras. Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
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