TABLE OF CONTENTS This appendix has been put in place mainly for the benefit of readers who may not be entirely familiar with group theory, or with square integrable group representations. To this end, we have collected here some essential abstract notions and results which underlie the concrete examples discussed in the book. However, this is by no means intended to be a crash course on group theory. There is a vast, indeed bewildering, amount of literature on groups, their representations and applications, pertinent to the subject matter of this book. The interested reader may wish to browse some of it, of which the following is just a small sampling: [Bar77, Cor84, Cor97, Gaa73] or [Gil74].
We begin with some basic notions, at a purely algebraic level. Examples appear in the next subsection.
A group is a set G on which there is defined a binary operation, usually called the group multiplication or group product mapping G G to G, ( g, g ?) 
gg ?, and obeying the following three axioms.
(G1) Associativity: for any g 1 , g 2 , g 3 ? G, one has
(G2) Neutral element: there exists a (necessarily unique) element e ? G such that
(G3) Inverse: every element g ? G possesses a unique inverse g ?1, such that
If in addition,
the group G is said to be abelian or
