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Part I of this book is a short review of the classical part of
representation theory. The main chapters of representation theory
are discussed: representations of finite and compact groups,
finite- and infinite-dimensional representations of Lie groups. It
is a typical feature of this survey that the structure of the
theory is carefully exposed - the reader can easily see the essence
of the theory without being overwhelmed by details. The final
chapter is devoted to the method of orbits for different types of
groups. Part II deals with representation of Virasoro and Kac-Moody
algebra. The second part of the book deals with representations of
Virasoro and Kac-Moody algebra. The wealth of recent results on
representations of infinite-dimensional groups is presented.
In its traditional form, Clifford analysis provides the function
theory for solutions of the Dirac equation. From the beginning,
however, the theory was used and applied to problems in other
fields of mathematics, numerical analysis, and mathematical
physics. recently, the theory has enlarged its scope considerably
by incorporating geometrical methods from global analysis on
manifolds and methods from representation theory. New, interesting
branches of the theory are based on conformally invariant,
first-order systems other than the Dirac equation, or systems that
are invariant with respect to a group other than the conformal
group. This book represents an up-to-date review of Clifford
analysis in its present form, its applications, and directions for
future research. Readership: Mathematicians and theoretical
physicists interested in Clifford analysis itself, or in its
applications to other fields.
One service mathematics has rendered the 'Et moil " '1 .i favait su
comment en revenir. je n'y scrais point all .. human race. It has
put oommon sense back Jules Verne when: it belongs, on the topmost
shelf next to the dusty canister labelled' discarded nonsense'. The
series is divergent; therefore we may be EricT.Bell able to do
something with it O. Heaviside Mathematics is a tool for thought A
highly necessary tool in a world where both feedback and nonlineari
ties abound. Similarly, all kinds of parts of mathematics serve as
tools for other parts and for other sci ences. Applying a simple
rewriting rule to the quote on the right above one finds such
statements as: 'One ser vice topology has rendered mathematical
physics .. .'; 'One service logic has rendered computer science ..
.'; 'One service category theory has rendered mathematics .. .'.
All arguably true. And all statements obtainable this way form part
of the raison d'etre of this series."
Part I of this book is a short review of the classical part of
representation theory. The main chapters of representation theory
are discussed: representations of finite and compact groups,
finite- and infinite-dimensional representations of Lie groups. It
is a typical feature of this survey that the structure of the
theory is carefully exposed - the reader can easily see the essence
of the theory without being overwhelmed by details. The final
chapter is devoted to the method of orbits for different types of
groups. Part II deals with representation of Virasoro and Kac-Moody
algebra. The second part of the book deals with representations of
Virasoro and Kac-Moody algebra. The wealth of recent results on
representations of infinite-dimensional groups is presented.
In its traditional form, Clifford analysis provides the function
theory for solutions of the Dirac equation. From the beginning,
however, the theory was used and applied to problems in other
fields of mathematics, numerical analysis, and mathematical
physics. recently, the theory has enlarged its scope considerably
by incorporating geometrical methods from global analysis on
manifolds and methods from representation theory. New, interesting
branches of the theory are based on conformally invariant,
first-order systems other than the Dirac equation, or systems that
are invariant with respect to a group other than the conformal
group. This book represents an up-to-date review of Clifford
analysis in its present form, its applications, and directions for
future research. Readership: Mathematicians and theoretical
physicists interested in Clifford analysis itself, or in its
applications to other fields.
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