A filtered category OS and applications /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Irving, Ronald S., 1952- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, 1990.
Colección:Memoirs of the American Mathematical Society ; Volume 83, no. 419.
Temas:
Verma modules.
Semisimple Lie groups.
Filtered modules.
Modules de Verma.
Groupes de Lie semi-simples.
Modules filtrés.
Filtered modules
Semisimple Lie groups
Verma modules
Acceso en línea:Texto completo
Tabla de Contenidos:
  • CONTENTS
  • I. INTRODUCTION
  • 1. INTRODUCTION
  • 1.1. Summary
  • 1.2. Filtered modules and filtered characters
  • 1.3. Projective and self-dual modules
  • 1.4. Overview of paper
  • 1.5. Acknowledgements
  • II. THE HECKE MODULE
  • 2. THE SIMPLE AND VERMA BASES
  • 2.1. Kazhdan-Lusztig polynomials
  • 2.2. The Hecke module: four equivalent definitions
  • 2.3. The Hecke module: proof of equivalences
  • 2.4. Duality and the simple basis
  • 2.5. The Hecke algebra action
  • 3. THE PROJECTIVE AND SELF-DUAL BASES
  • 3.1. The projective basis
  • 3.2. Some elements of the Hecke algebra3.3. An involution of M[sup(*)]sub(s)]
  • 3.4. A new self-dual basis
  • 4. THE SPECIALIZED HECKE MODULE
  • 4.1. Definitions
  • 4.2. Duality polynomials
  • 4.3. A Jantzen sum formula
  • III. THE FILTERED CATEGORY O[sub(s)]
  • 5. THE CATEGORY O AND TRANSLATION FUNCTORS
  • 5.1. The category and its Grothendieck group
  • 5.2. Translation functors
  • 6. THE FILTERED CATEGORY O[sub(s)] AND TRANSLATION FUNCTORS
  • 6.1. Definition and basic properties of the filtered category
  • 6.2. Some important filtrations
  • 6.3. Translation functors on the filtered categoryIV. APPLICATIONS
  • 7. RADICAL FILTRATIONS OF GENERALIZED VERMA MODULES AND PROJECTIVE MODULES
  • 7.1. Radical filtrations of generalized Verma modules
  • 7.2. Radical filtrations of projective indecomposable modules
  • 7.3. More on radical filtrations
  • 7.4. Rigidity of generalized Verma modules and projective modules
  • 8. SELF-DUAL PROJECTIVE MODULES AND THEIR FILTERED CHARACTERS
  • 8.1. Self-dual projective modules: review
  • 8.2. Filtered self-duality of certain projective modules
  • 8.3. Applications
  • 9. SELF-DUAL MODULES WITH A VERMA FLAG AND THEIR FILTERED CHARACTERS9.1. A class of self-dual modules with a Verma flag
  • 9.2. A category of self-dual modules
  • REFERENCES

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