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Symmetry, representations, and invariants

Symmetry, representations, and invariants (Loan 2 times)

Material type
단행본
Personal Author
Goodman, Roe. Wallach, Nolan R. Wallach, Nolan R.
Title Statement
Symmetry, representations, and invariants / Roe Goodman, Nolan R. Wallach.
Publication, Distribution, etc
Dordrecht :   Springer,   c2010.  
Physical Medium
xx, 716 p. ; 24 cm.
Series Statement
Graduate texts in mathematics ;255
ISBN
9781441927293
요약
"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 More than 350 exercises (most with detailed hints for solutions) further explore main concepts. Serves as an excellent main text for a one-year course in Lie group theory Benefits physicists as well as mathematicians as a reference work. 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 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. 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 and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: - 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 - More than 350 exercises (most with detailed hints for solutions) further explore main concepts - Serves as an excellent main text for a one-year course in Lie group theory - Benefits physicists as well as mathematicians as a reference work."--Publisher's website.
General Note
"Symmetry, in the title of this book, should be understood as the geometry of Lie (and algebraic) group actions"--Page xv.  
"Based on 'Representations and invariants of the classical groups', Roe Goodman and Nolan R. Wallach, Cambridge University Press, 1998, third corrected printing 2003"--Page [iv].  
Content Notes
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.
Bibliography, Etc. Note
Includes bibliographical references and indexes. Includes bibliographical references (pages 697-703) and indexes.
Subject Added Entry-Topical Term
Representations of groups. Invariants. Symmetry (Mathematics). Lie groups. Algebra.
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100 1 ▼a Goodman, Roe.
245 1 0 ▼a Symmetry, representations, and invariants / ▼c Roe Goodman, Nolan R. Wallach.
260 ▼a Dordrecht : ▼b Springer, ▼c c2010.
300 ▼a xx, 716 p. ; ▼c 24 cm.
490 1 ▼a Graduate texts in mathematics ; ▼v 255
500 ▼a "Symmetry, in the title of this book, should be understood as the geometry of Lie (and algebraic) group actions"--Page xv.
500 ▼a "Based on 'Representations and invariants of the classical groups', Roe Goodman and Nolan R. Wallach, Cambridge University Press, 1998, third corrected printing 2003"--Page [iv].
504 ▼a Includes bibliographical references and indexes.
504 ▼a Includes bibliographical references (pages 697-703) and indexes.
505 0 ▼a 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.
520 ▼a "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 More than 350 exercises (most with detailed hints for solutions) further explore main concepts. Serves as an excellent main text for a one-year course in Lie group theory Benefits physicists as well as mathematicians as a reference work. 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 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. 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 and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: - 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 - More than 350 exercises (most with detailed hints for solutions) further explore main concepts - Serves as an excellent main text for a one-year course in Lie group theory - Benefits physicists as well as mathematicians as a reference work."--Publisher's website.
650 0 ▼a Representations of groups.
650 0 ▼a Invariants.
650 0 ▼a Symmetry (Mathematics).
650 0 ▼a Lie groups.
650 0 ▼a Algebra.
700 1 ▼a Wallach, Nolan R.
700 1 ▼a Wallach, Nolan R.
830 0 ▼a Graduate texts in mathematics ; ▼v 255.
945 ▼a KLPA

Holdings Information

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No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.55 G653s Accession No. 121252754 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of 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.

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