Symmetry, representations, and invariants / Roe Goodman, Nolan R. Wallach

Author: Goodman, Roe
Published: Dordrecht [Netherlands] ; New York : Springer, [2009]
Copyright Date: ©2009
Physical Description: xx, 716 pages : illustrations ; 24 cm.
Additional Creators: Wallach, Nolan R.

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Series

Graduate texts in mathematics ; 255

Contents

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(V) -- Tensor representations of O(V) and Sp(V) -- Algebraic groups and homogeneous spaces -- Representations on spaces of regular functions -- Algebraic geometry -- Linear and multilinear algebra -- Associative algebras and lie algebras -- Manifolds and Lie groups.

Summary

"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 work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications." --Book Jacket.

Subject(s)

ISBN

9780387798516 (acid-free paper)
038779851X (acid-free paper)
9780387798523 (e-ISBN)
0387798528 (e-ISBN)
1441927298
9781441927293

Note

"Symmetry, in the title of this book, should be understood as the geometry of Lie (and algebraic) group actions"--P. xv.
"Based on 'Representations and invariants of the classical groups', Roe Goodman and Nolan R. Wallach, Cambridge University Press, 1998, third corrected printing 2003"--P. [iv].

Bibliography Note

Includes bibliographical references (pages 697-703) and indexes.

View MARC record | catkey: 7406141