Algebraic Structures and Operator Calculus

About this book

This is the last of three volumes which present, in an original way, some of the most important tools of applied mathematics, in areas such as probability theory, operator calculus, representation theory, and special functions, used in solving problems in mathematics, physics and computer science. This third volume - Representations of Lie Groups - answers some basic questions, like 'how can a Lie algebra given in matrix terms, or by prescribed commutation relations be realised so as to give an idea of what it 'looks like'?' A concrete theory is presented with emphasis on techniques suitable for efficient symbolic computing. Another question is 'how do classical mathematical constructs interact with Lie structures?' Here stochastic processes are taken as an example. The volume concludes with a section on output of the MAPLE program, which is available from Kluwer Academic Publishers on the Internet. Audience : This book is intended for pure and applied mathematicians and theoretical computer scientists. It is suitable for self study by researchers, as well as being appropriate as a text for a course or advanced seminar.