文档介绍：Jing-Song Huang
Pavle Pandziˇ c´
Dirac Operators in
Representation Theory
Birkhauser¨
Boston • Basel • Berlin
Jing-Song Huang Pavle Pandziˇ c´
The Hong Kong University of University of Zagreb
Science and Technology Department of Mathematics
Department of Mathematics 10002 Zagreb
Clear Water Bay, Kowloon Croatia
Hong Kong, .
Mathematics Subject Classification (2000): 22E46
Library of Congress Control Number: 2006923127
ISBN-10 0-8176-3218-2 e-IBSN 0-8176-4493-8
ISBN-13 978-0-8176-3218-2
Printed on acid-free paper.
c 2006 Birkhauser¨ Boston
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Preface
We begin with the origin of the Dirac equation and give a brief introduction of the
Dirac operators due to Parthasarathy, Vogan and Kostant. Then we explain a conjec-
ture of Vogan on Dirac cohomology, which we proved in [HP1], its applications and
anization of the book.
The Dirac equation. The Dirac equation has an interesting connection to
E = mc2, the Einstein’s equation from his special theory of relativity. This equa-
tion relates the energy E of a particle at rest to its mass m through a conversion
factor, the square of the speed c of light. However, this way of writing