The Resource Combinatorics of minuscule representations, R.M. Green, (electronic resource)

Combinatorics of minuscule representations, R.M. Green, (electronic resource)

Label
Combinatorics of minuscule representations
Title
Combinatorics of minuscule representations
Statement of responsibility
R.M. Green
Creator
Subject
Genre
Language
eng
Summary
Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Green, R. M
Dewey number
511.6
Illustrations
illustrations
Index
index present
LC call number
QA164
LC item number
.G74 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
  • Cambridge tracts in mathematics
  • Cambridge Tracts in Mathematics
Series volume
199
http://library.link/vocab/subjectName
  • Combinatorial analysis
  • Lie algebras
  • Weyl groups
Label
Combinatorics of minuscule representations, R.M. Green, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Contents; Introduction; 1 Classical Lie algebras and Weyl groups; 1.1 Lie algebras; 1.2 The classical Lie algebras; 1.3 Classical Lie algebras and partially ordered sets; 1.4 Classical Weyl groups and partially ordered sets; 1.5 Notes and references; 2 Heaps over graphs; 2.1 Basic definitions; 2.2 Full heaps over Dynkin diagrams; 2.3 Local structure of full heaps; 2.4 Quotient heaps; 2.5 Notes and references; 3 Weyl group actions; 3.1 Linear operators and group actions; 3.2 Proper ideals; 3.3 Parabolic subheaps; 3.4 Notes and references; 4 Lie theory
  • 4.1 Representations of Lie algebras from heaps4.2 Review of Lie theory; 4.3 Review of Weyl groups; 4.4 Strongly orthogonal sets; 4.5 Notes and references; 5 Minuscule representations; 5.1 Highest weight modules; 5.2 Weights and heaps; 5.3 Periodicity and trivialization; 5.4 Reflections; 5.5 Minuscule representations from heaps; 5.6 Invariant bilinear forms; 5.7 Notes and references; 6 Full heaps over affine Dynkin diagrams; 6.1 Full heaps in type Al(1); 6.2 Proper ideals in type Al(1); 6.3 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 The classification of full heaps over affine Dynkin diagrams6.7 Notes and references; 7 Chevalley bases; 7.1 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 Notes and references; 8 Combinatorics of Weyl groups; 8.1 Minuscule systems; 8.2 Weyl groups as permutation groups; 8.3 Ideals of roots; 8.4 Weight polytopes; 8.5 Faces of weight polytopes; 8.6 Graphs from minuscule representations; 8.7 Notes and references; 9 The 28 bitangents; 9.1 The Gosset graph
  • 9.2 Del Pezzo surfaces9.3 Bitangents; 9.4 Hesse-Cayley notation; 9.5 Steiner complexes; 9.6 Symplectic structure; 9.7 Notes and references; 10 Exceptional structures; 10.1 The 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; 11 Further topics; 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 Notes and references; Appendix A: Posets, graphs and categories; A.1 Posets and graphs; A.2 Categories
  • Appendix B: Lie theoretic dataReferences; Index
Dimensions
unknown
Extent
1 online resource (330 p.)
Form of item
online
Isbn
9781299009066
Media category
computer
Media MARC source
rdamedia
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000329901
  • (EBL)1113083
  • (OCoLC)827210322
  • (UkCbUP)CR9781139207003
  • (MiAaPQ)EBC1113083
  • (EXLCZ)992670000000329901
Label
Combinatorics of minuscule representations, R.M. Green, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Contents; Introduction; 1 Classical Lie algebras and Weyl groups; 1.1 Lie algebras; 1.2 The classical Lie algebras; 1.3 Classical Lie algebras and partially ordered sets; 1.4 Classical Weyl groups and partially ordered sets; 1.5 Notes and references; 2 Heaps over graphs; 2.1 Basic definitions; 2.2 Full heaps over Dynkin diagrams; 2.3 Local structure of full heaps; 2.4 Quotient heaps; 2.5 Notes and references; 3 Weyl group actions; 3.1 Linear operators and group actions; 3.2 Proper ideals; 3.3 Parabolic subheaps; 3.4 Notes and references; 4 Lie theory
  • 4.1 Representations of Lie algebras from heaps4.2 Review of Lie theory; 4.3 Review of Weyl groups; 4.4 Strongly orthogonal sets; 4.5 Notes and references; 5 Minuscule representations; 5.1 Highest weight modules; 5.2 Weights and heaps; 5.3 Periodicity and trivialization; 5.4 Reflections; 5.5 Minuscule representations from heaps; 5.6 Invariant bilinear forms; 5.7 Notes and references; 6 Full heaps over affine Dynkin diagrams; 6.1 Full heaps in type Al(1); 6.2 Proper ideals in type Al(1); 6.3 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 The classification of full heaps over affine Dynkin diagrams6.7 Notes and references; 7 Chevalley bases; 7.1 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 Notes and references; 8 Combinatorics of Weyl groups; 8.1 Minuscule systems; 8.2 Weyl groups as permutation groups; 8.3 Ideals of roots; 8.4 Weight polytopes; 8.5 Faces of weight polytopes; 8.6 Graphs from minuscule representations; 8.7 Notes and references; 9 The 28 bitangents; 9.1 The Gosset graph
  • 9.2 Del Pezzo surfaces9.3 Bitangents; 9.4 Hesse-Cayley notation; 9.5 Steiner complexes; 9.6 Symplectic structure; 9.7 Notes and references; 10 Exceptional structures; 10.1 The 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; 11 Further topics; 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 Notes and references; Appendix A: Posets, graphs and categories; A.1 Posets and graphs; A.2 Categories
  • Appendix B: Lie theoretic dataReferences; Index
Dimensions
unknown
Extent
1 online resource (330 p.)
Form of item
online
Isbn
9781299009066
Media category
computer
Media MARC source
rdamedia
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000329901
  • (EBL)1113083
  • (OCoLC)827210322
  • (UkCbUP)CR9781139207003
  • (MiAaPQ)EBC1113083
  • (EXLCZ)992670000000329901

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