Introduction to The Theory of Nonsymmetric Dirichlet Forms

The theory of toric varieties (also called torus embeddings) describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications found since toric varieties were introduced in the early 1970's.

Symmetry plays an essential role in science - not only in crystallography and quantum theory, where its role has long been explicitly recognized, but also in condensed-matter physics, thermodynamics, chemistry, biology, and others. This text discusses the concept of symmetry and its application to many areas of science. While it includes a detailed introduction to the theory of groups, which forms the mathematical apparatus for describing symmetries, it also includes a much more general discussion of the nature of symmetry and its role in science. Many problems serve to sharpen the reader's understanding, and an extensive bibliography concludes the book.

The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory.