R. M. Green - Böcker

This well-established textbook gives a general but comprehensive introduction to positional astronomy. Originally based on the author's lecture courses at Cambridge University, it is intended primarily for undergraduates, but, due to its comprehensive nature, it is a very useful reference text for research workers in many branches of astronomy and space physics. The author considers the night sky as the celestial sphere and powerfully exploits the methods of spherical geometry. Most problems in which the precise determination of a heavenly body's position in the sky is important are considered in theoretical detail, and the necessary formulae are derived to a precision that is sufficient for all but the most specialist purposes. The present revision has ensured that the terminology and treatment correspond precisely to current astronomical practice. A guiding principle has been to re-establish compatibility with the Astronomical Ephemeris and, to a lesser extent, with the fuller explanations of the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. Fairly frequent comments added to the text indicate the sometimes modified relevance of the subject matter to modern astronomy. A number of additional exercises help to illustrate the new material.

Minuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book describes a combinatorial approach to minuscule representations of Lie algebras using the theory of heaps, which for most practical purposes can be thought of as certain labelled partially ordered sets. This leads to uniform constructions of (most) simple Lie algebras over the complex numbers and their associated Weyl groups, and provides a common framework for various applications. The topics studied include Chevalley bases, permutation groups, weight polytopes and finite geometries. Ideal as a reference, this book is also suitable for students with a background in linear and abstract algebra and topology. Each chapter concludes with historical notes, references to the literature and suggestions for further reading.