Representations of Permutation Groups II
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495 Adalbert Kerber
Representations of Permutation Groups II
Springer-Verlag Berlin.Heidelberg. New York 1975
Autor Prof. Dr. Adalbert Kerber Lehrstuhl D fiJr Mathematik Rhein.-Westf. Technische Hochschule Aachen Templergraben 55 51 Aachen/BRD
Library of Congress Cataloging in Publication Data
Kerber, Adalbert. Representations of permutation groups I-II. (Lecture notes in mathematies, 240, 495) Bibliography: p. Includes indexes. CONTENTS: pt. I. Representation of wreath products and applications to the representation theory of symmetric and alternating groups. i. Permutation groups. 2. Representations of groups. I. Title. II. Series: Lecture notes in mathematics (Berlin), 240, etc. QA3.L28 no. 240, etc. 510'.8s [512'.2] 72-183956
AMS Subject Classifications (1970): 05 A15, 20 C30 ISBN 3-540-07535-6 Springer-Verlag Berlin Heidelberg 9 New 9 York ISBN 0-387-07535-6 Springer-Verlag New Y o r k . Heidelberg Berlin 9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under w 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 9 by Springer-Verlag Berlin Heidelberg 9 1975 Printed in Germany Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
Preface
The d e s c r i p t i o n of the r e p r e s e n t a t i o n theory of w r e a t h products and its a p p l i c a t i o n s
are continued
in this second part.
In part I the emphasis
lay on the c o n s t r u c t i o n
matrix r e p r e s e n t a t i o n s
of w r e a t h p r o d u c t s
closed field.
In part
cible characters part
of the irreducible
over an a l g e b r a i c a l l y
II, I consider mainly the o r d i n a r y
of these groups, which were
irredu-
less important
in
I.
The c o n s i d e r a t i o n s presentations,
apply especially
to the s y m m e t r i z a t i o n of re-
so that we obtain quite easily famous results
Schur, Frobenius,
Weyl and van der W a e r d e n about the c o n n e c t i o n
b e t w e e n the r e p r e s e n t a t i o n theories tric groups.
of general
linear and symme-
They apply also to the theory of e n u m e r a t i o n under
group action so that we obtain the most theory,
important
results of this
which has been d e v e l o p e d mainly by Redfield,
de Bruijn.
of
This theory
torics and it yields
is nowadays
an essential part
the main e n u m e r a t i o n techniques
P61ya and of combinain graph
theory. These applications
and some related topics
are d i s c u s s e d here.
In the first sections the main r e s u l t s needed from part quoted,
so that this part
is in a sense also selfcontained.
I would like to express my sincerest who work in that
I are
thanks to many colleagues
field and in p a r t i c u l a r to the people w o r k
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