The Resource Combinatorics of minuscule representations, R.M. Green

Combinatorics of minuscule representations, R.M. Green

Label
Combinatorics of minuscule representations
Title
Combinatorics of minuscule representations
Statement of responsibility
R.M. Green
Creator
Subject
Language
eng
Summary
"Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"--
Member of
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorDate
1971-
http://library.link/vocab/creatorName
Green, R. M.
Dewey number
512/.482
Index
index present
LC call number
QA252.3
LC item number
.G74 2013
Literary form
non fiction
Nature of contents
bibliography
Series statement
Cambridge tracts in mathematics
Series volume
199
http://library.link/vocab/subjectName
  • Representations of Lie algebras
  • Combinatorial analysis
Label
Combinatorics of minuscule representations, R.M. Green
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Classical Weyl groups and partially ordered sets
  • Bitangents
  • 9.4.
  • Hesse-Cayley notation
  • 9.5.
  • Steiner complexes
  • 9.6.
  • Symplectic structure
  • 9.7.
  • Notes and references
  • 10.1.
  • 1.5.
  • 27 lines on a cubic surface
  • 10.2.
  • Combinatorics of double sixes
  • 10.3.
  • 2-graphs
  • 10.4.
  • Generalized quadrangles
  • 10.5.
  • Higher invariant forms
  • 10.6.
  • Notes and references
  • Notes and references
  • 11.1.
  • Minuscule elements of Weyl groups
  • 11.2.
  • Principal subheaps as abstract posets
  • 11.3.
  • Gaussian posets
  • 11.4.
  • Jeu de taquin
  • 11.5.
  • 2.1.
  • Notes and references
  • Basic definitions
  • 2.2.
  • Full heaps over Dynkin diagrams
  • 2.3.
  • Local structure of full heaps
  • 2.4.
  • Machine generated contents note:
  • Quotient heaps
  • 2.5.
  • Notes and references
  • 3.1.
  • Linear operators and group actions
  • 3.2.
  • Proper ideals
  • 3.3.
  • Parabolic subheaps
  • 3.4.
  • 1.1.
  • Notes and references
  • 4.1.
  • Representations of Lie algebras from heaps
  • 4.2.
  • Review of Lie theory
  • 4.3.
  • Review of Weyl groups
  • 4.4.
  • Strongly orthogonal sets
  • 4.5.
  • Lie algebras
  • Notes and references
  • 5.1.
  • Highest weight modules
  • 5.2.
  • Weights and heaps
  • 5.3.
  • Periodicity and trivialization
  • 5.4.
  • Reflections
  • 5.5.
  • 1.2.
  • Minuscule representations from heaps
  • 5.6.
  • Invariant bilinear forms
  • 5.7.
  • Notes and references
  • 6.1.
  • Full heaps in type Al(1)
  • 6.2.
  • Proper ideals in type Al(1)
  • 6.3.
  • classical Lie algebras
  • Spin representations in type Dl
  • 6.4.
  • Types Bl(1) and Dl+1(2)
  • 6.5.
  • Full heaps in type E6(1) and E7(1)
  • 6.6.
  • classification of full heaps over affine Dynkin diagrams
  • 6.7.
  • Notes and references
  • 7.1.
  • 1.3.
  • Kac's asymmetry function
  • 7.2.
  • Relations in simply laced simple Lie algebras
  • 7.3.
  • Folding
  • 7.4.
  • Long and short roots
  • 7.5.
  • Relations in non-simply laced simple Lie algebras
  • 7.6.
  • Classical Lie algebras and partially ordered sets
  • Notes and references
  • 8.1.
  • Minuscule systems
  • 8.2.
  • Weyl groups as permutation groups
  • 8.3.
  • Ideals of roots
  • 8.4.
  • Weight polytopes
  • 8.5.
  • 1.4.
  • Faces of weight polytopes
  • 8.6.
  • Graphs from minuscule representations
  • 8.7.
  • Notes and references
  • 9.1.
  • Gosset graph
  • 9.2.
  • Del Pezzo surfaces
  • 9.3.
Dimensions
24 cm.
Extent
vii, 320 p.
Isbn
9781107026247
Isbn Type
(hardback)
Lccn
2012042963
System control number
  • (CaMWU)u2897872-01umb_inst
  • 2745792
  • (Sirsi) i9781107026247
  • (OCoLC)815364932
Label
Combinatorics of minuscule representations, R.M. Green
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Classical Weyl groups and partially ordered sets
  • Bitangents
  • 9.4.
  • Hesse-Cayley notation
  • 9.5.
  • Steiner complexes
  • 9.6.
  • Symplectic structure
  • 9.7.
  • Notes and references
  • 10.1.
  • 1.5.
  • 27 lines on a cubic surface
  • 10.2.
  • Combinatorics of double sixes
  • 10.3.
  • 2-graphs
  • 10.4.
  • Generalized quadrangles
  • 10.5.
  • Higher invariant forms
  • 10.6.
  • Notes and references
  • Notes and references
  • 11.1.
  • Minuscule elements of Weyl groups
  • 11.2.
  • Principal subheaps as abstract posets
  • 11.3.
  • Gaussian posets
  • 11.4.
  • Jeu de taquin
  • 11.5.
  • 2.1.
  • Notes and references
  • Basic definitions
  • 2.2.
  • Full heaps over Dynkin diagrams
  • 2.3.
  • Local structure of full heaps
  • 2.4.
  • Machine generated contents note:
  • Quotient heaps
  • 2.5.
  • Notes and references
  • 3.1.
  • Linear operators and group actions
  • 3.2.
  • Proper ideals
  • 3.3.
  • Parabolic subheaps
  • 3.4.
  • 1.1.
  • Notes and references
  • 4.1.
  • Representations of Lie algebras from heaps
  • 4.2.
  • Review of Lie theory
  • 4.3.
  • Review of Weyl groups
  • 4.4.
  • Strongly orthogonal sets
  • 4.5.
  • Lie algebras
  • Notes and references
  • 5.1.
  • Highest weight modules
  • 5.2.
  • Weights and heaps
  • 5.3.
  • Periodicity and trivialization
  • 5.4.
  • Reflections
  • 5.5.
  • 1.2.
  • Minuscule representations from heaps
  • 5.6.
  • Invariant bilinear forms
  • 5.7.
  • Notes and references
  • 6.1.
  • Full heaps in type Al(1)
  • 6.2.
  • Proper ideals in type Al(1)
  • 6.3.
  • classical Lie algebras
  • Spin representations in type Dl
  • 6.4.
  • Types Bl(1) and Dl+1(2)
  • 6.5.
  • Full heaps in type E6(1) and E7(1)
  • 6.6.
  • classification of full heaps over affine Dynkin diagrams
  • 6.7.
  • Notes and references
  • 7.1.
  • 1.3.
  • Kac's asymmetry function
  • 7.2.
  • Relations in simply laced simple Lie algebras
  • 7.3.
  • Folding
  • 7.4.
  • Long and short roots
  • 7.5.
  • Relations in non-simply laced simple Lie algebras
  • 7.6.
  • Classical Lie algebras and partially ordered sets
  • Notes and references
  • 8.1.
  • Minuscule systems
  • 8.2.
  • Weyl groups as permutation groups
  • 8.3.
  • Ideals of roots
  • 8.4.
  • Weight polytopes
  • 8.5.
  • 1.4.
  • Faces of weight polytopes
  • 8.6.
  • Graphs from minuscule representations
  • 8.7.
  • Notes and references
  • 9.1.
  • Gosset graph
  • 9.2.
  • Del Pezzo surfaces
  • 9.3.
Dimensions
24 cm.
Extent
vii, 320 p.
Isbn
9781107026247
Isbn Type
(hardback)
Lccn
2012042963
System control number
  • (CaMWU)u2897872-01umb_inst
  • 2745792
  • (Sirsi) i9781107026247
  • (OCoLC)815364932

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