Geometric complexity theory IV : nonstandard quantum group for the Kronecker problem /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Blasiak, Jonah, 1982- (Autor), Mulmuley, Ketan (Autor), Sohoni, Milind, 1969- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 2014.
Colección:Memoirs of the American Mathematical Society ; Volume 235, no. 1109 (fourth of 5 numbers)
Temas:
Combinatorial analysis.
Kronecker products.
Analyse combinatoire.
Produits de Kronecker.
Combinatorial analysis
Kronecker products
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • 1.1. The Kronecker problem
  • 1.2. The basis-theoretic version of the Kronecker problem
  • 1.3. Canonical bases connect quantum Schur-Weyl duality with RSK
  • 1.4. The nonstandard quantum group and Hecke algebra
  • 1.5. Towards an upper canonical basis for \nsbr{ }^{\tsr }
  • 1.6. The approach of Adsul, Sohoni, and Subrahmanyam
  • 1.7. A global crystal basis for \nsbr{ }_{ }
  • 1.8. Organization
  • Chapter 2. Basic concepts and notation
  • 2.1. General notation
  • 2.2. Tensor products
  • 2.3. Words and tableaux2.4. Cells
  • 2.5. Comodules
  • 2.6. Dually paired Hopf algebras
  • Chapter 3. Hecke algebras and canonical bases
  • 3.1. The upper canonical basis of â??()
  • 3.2. Cells in type
  • Chapter 4. The quantum group _{ }()
  • 4.1. The quantized enveloping algebra \Uq
  • 4.2. FRT-algebras
  • 4.3. The quantum coordinate algebra Ã?(_{ }())
  • 4.4. The quantum determinant and the Hopf algebra Ã?(_{ }())
  • 4.5. A reduction system for Ã?(_{ }())
  • 4.6. Compactness, unitary transformations
  • 4.7. Representations of _{ }()Chapter 5. Bases for _{ }() modules
  • 5.1. Gelfand-Tsetlin bases and Clebsch-Gordon coefficients
  • 5.2. Crystal bases
  • 5.3. Global crystal bases
  • 5.4. Projected based modules
  • 5.5. Tensor products of based modules
  • Chapter 6. Quantum Schur-Weyl duality and canonical bases
  • 6.1. Commuting actions on \bT= ^{\tsr }
  • 6.2. Upper canonical basis of \bT
  • 6.3. Graphical calculus for _{ }(\glâ??)-modules
  • Chapter 7. Notation for _{ }()Ã? _{ }()
  • Chapter 8. The nonstandard coordinate algebra (â?³_{ }())8.1. Definition of Ã?(_{ }(\nsbr{ }))
  • 8.2. Nonstandard symmetric and exterior algebras
  • 8.3. Explicit product formulae
  • 8.4. Examples and computations for Ã?(_{ }(\nsbr{ }))
  • Chapter 9. Nonstandard determinant and minors
  • 9.1. Definitions
  • 9.2. Nonstandard minors in the two-row case
  • 9.3. Symmetry of the determinants and minors
  • 9.4. Formulae for nonstandard minors
  • Chapter 10. The nonstandard quantum groups _{ }() and _{ }()
  • 10.1. Hopf structure
  • 10.2. Compact real form10.3. Complete reducibility
  • Chapter 11. The nonstandard Hecke algebra â??áæ£
  • 11.1. Definition of \nsHáæ£ and basic properties
  • 11.2. Semisimplicity of \field\nsHáæ£
  • 11.3. Representation theory of ²â??áæ£
  • 11.4. Some representation theory of \nsHáæ£
  • 11.5. The sign representation in the canonical basis
  • 11.6. The algebra \nsHâ??
  • 11.7. A canonical basis of \nsHâ??
  • 11.8. The algebra \nsHâ??
  • Chapter 12. Nonstandard Schur-Weyl duality
  • 12.1. Nonstandard Schur-Weyl duality

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