The Representation Theory of the Symmetric Groups
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682 G. D. James
The Representation Theory of the Symmetric Groups
Springer-Verlag Berlin Heidelberg New York 1978
Author G. D. James Sidney Sussex College Cambridge CB2 3HU Great Britain
AMS Subject Classifications (1970): 20C15, 20C20, 20C30
ISBN 3-540-08948-9 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08948-9 Springer-Verlag New York Heidelberg Berlin 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 § 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.
© by Springer-Verlag Berlin Heidelberg 1978 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Pre::ace The representation theory of the symmetric groups was first studied by Frobenius and Schur, and then developed in a long series of papers by Young.
Althouqh a detailed study of Young's work would undoubtedly
Day dividends, anyone who has attemnted this will realize just how difficult it is to read his papers.
The author, for one, has never
undertaken this task, and so no reference will be found here to any of Young's proofs, although it is probable that some of the techniques presented are identical to his. These notes are based on those given for a Part III course at Cambridge in 1977, and include all the basic theorems in the subject, as well as some material previous Iv unpUblished. are easier to explain
Many of the results
a blackboard and chalk than with the type-
written word, since combinatorial arguments can often be best presented to a student bv indicating the correct line, and leaving him to write out a comnlete proof if he wishes.
In many places of this book we have
nreceded a proof bv a worked example, on the nrinciple that the reader will learn more easily bv translating for himself from the particular to the general than by reading the sometimes unpleasant notation reqUired for a full proof.
However, the complete argument is always inclUded,
perhaps at the expense of supnlying details which the reader might find quicker to check for himself.
This is especially important when dealing
with one of the central theorems,
as the LittlewoodRichardson
Rule, since many who read early proofs of this Rule find it difficult to fill in the details (see [16] for a description of the problems encountered) • The aDproach adopted is characteristicfree, except in those places, such as the construction of the character tables of symmetric qrouus, where the results themselves deDend upon the ground field.
The
reader who is not familiar with representation theory over arbitrary fields must not be deterred by this; we believe, in fact, that the ordinary reDresentation theory is easier to understand by looking initially
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