Symmetry, representations, and invariants

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work bythe authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentationthat is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples anddiscussion prepares the reader for the complete arguments now given in the general case. Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux) Self-contained chapters, appendices, comprehensive bibliography INDICE: Preface.- Organization and Notation.- Lie Groups and Algebraic Groups.- Structure of Classical Groups.- Highest-Weight Theory.- Algebras and Representations.- Classical Invariant Theory.- Spinors.- Character Formulas.- Branching Laws.- Tensor Representations of GL(n).- Tensor Representations of O(V)and Sp(V).- Algebraic Groups and Homogeneous Spaces.- Representations on Function Spaces.- Algebraic Geometry.- Linear and Multilinear Algebra.- Associative Algebras and Lie Algebras.- Manifolds and Lie Groups.- References.- Index ofSymbols.- Subject Index.

• ISBN: 978-0-387-79851-6
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 716
• Fecha Publicación: 01/06/2009
• Nº Volúmenes: 1
• Idioma: Inglés