Spin Representations of \(\mathfrak{s}{\mathfrak{d}_m}\mathbb{C}\)
In this lecture we complete the picture of the representations of the orthogonal Lie algebras by constructing the spin representations\({S^ \pm }\) of\(\mathfrak{s}{\mathfrak{d}_m}\mathbb{C}\) this also yields a description of the spin groups\(Spi{n_m}\ma
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Editorial Board
S. Axler
EW. Gehring
K.A. Ribet
Graduate Texts in Mathematics
Readings in Mathematics
EbbinghausIHermeslHirzebruchlKoecherlMainzerlNeukirchlPresteVRemmert: Numbers FultonlHarris: Representation Theory: AFirst Course Murty: Problems in Analytic Number Theory Remmert: TheoryofComplex Functions Walter: Ordinary DifJerential Equations
Undergraduate Texts in Mathematics
Readings in Mathematics
Anglin: Mathematics: A Concise History and Philosophy Anglin!Lambek: The Heritage of Thales Bressoud: Second Year Calculus HairerlWanner: Analysis by Its History HlImmerlinlHoffinann: Numerical Mathematics Isaac: The Pleasures of Probability Laubenbacher/Pengelley: Mathematical Expeditions: Chronicles by the Explorers Samuel: Projective Geometry Stillwell: Numbers and Geometry Toth: Glimpses ofAlgebra and Geometry
William Fulton Joe Harris
Representation Theory A First Course With 144 Illustrations
~ Springer
William Fulton Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA [email protected]
Joe Harris Department of Mathematics Harvard University Cambridge, MA 02138 USA [email protected]
Editorial Board S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA
EW. Gehring Mathematics Department East HaU University of Michigan Ann Arbor, MI 48109 USA
K.A. Ribet Mathematics Depa11ment University of California at Berkeley Berkeley, CA 94720-3840 USA
Mathematies Subjeet Classifieation (2000): 20G05, 17BI0, 17B20, 22E46 Library of Congress Cataloging-in-Publieation Data Fulton, William, 1939Representation theory: a first eourse / William Fulton and Joe Harris. p. em. - (Graduate texts in mathematies) IncJudes bibliographieal referenees and index. 1. Representations of groups. 2. Representations of Algebras. 3. Lie Groups. 4. Lie algebras. 1. Harris, Joe. II. Tîtle. III. Series. QA171.F85 1991 512'.2--dc20 90-24926 ISBN 978-1-4612-0979-9 (eBook) ISBN 978-0-387-97495-8 DOI 10.1007/978-1-4612-0979-9 Printed on acid-free paper.
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Preface
The primary goal of these lectures is to introduce a beginner to the finitedimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in
