
The Fourfold Way in Real Analysis
An Alternative to the Metaplectic Representation
André Unterberger(Author)
Birkhäuser (Publisher)
Published on 17. March 2006
Book
Hardback
X, 222 pages
978-3-7643-7544-7 (ISBN)
Description
The n-dimensionalmetaplectic groupSp(n,R) is the twofoldcoverof the sympl- n n tic group Sp(n,R), which is the group of linear transformations ofX = R xR that preserve the bilinear (alternate) form x y [( ), ( )] =? x, ? + y, ? . (0. 1) ? ? 2 n There is a unitary representation of Sp(n,R)intheHilbertspace L (R ), called the metaplectic representation,the image of which is the groupof transformations generated by the following ones: the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier transformation; some normalization factor enters the de?- tion of the operators of the ?rst and third species. The metaplectic representation was introduced in a great generality in [28] - special cases had been considered before, mostly in papers of mathematical physics - and it is of such fundamental importancethat the two concepts (the groupand the representation)havebecome virtually indistinguishable. This is not going to be our point of view: indeed, the main point of this work is to show that a certain ?nite covering of the symplectic group (generally of degree n) has another interesting representation, which enjoys analogues of most of the nicer properties of the metaplectic representation.
We shall call it the anaplectic representation - other coinages that may come to your mind sound too medical - and shall consider ?rst the one-dimensional case, the main features of which can be described in quite elementary terms.
We shall call it the anaplectic representation - other coinages that may come to your mind sound too medical - and shall consider ?rst the one-dimensional case, the main features of which can be described in quite elementary terms.
More details
Series
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
X, 222 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
1120 gr
ISBN-13
978-3-7643-7544-7 (9783764375447)
DOI
10.1007/3-7643-7545-0
Schweitzer Classification
Other editions
Additional editions

E-Book
06/2006
1st Edition
Birkhäuser
€53.49
Available for download
Content
The One-dimensional Anaplectic Representation.- The n-dimensional Anaplectic Analysis.- Towards the Anaplectic Symbolic Calculi.- The One-dimensional Case Revisited.