A filtered category OS and applications / / Ronald S. Irving

• Record Nr.: UNINA9910480580403321
• Autore: Irving Ronald S. <1952->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 1990; ©1990
• ISBN: 1-4704-0842-2
• Descrizione fisica: 1 online resource (131 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 83, Number 419
• Disciplina: 512/.2
• Soggetti: Verma modules; Semisimple Lie groups; Filtered modules; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "January 1990, volume 83, number 419 (first of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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 algebra""""3.3. 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 category""""IV. ; 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 CHARACTERS""""9.1. A class of self-dual modules with a Verma flag""; ""9.2. A category of self-dual modules""; ""REFERENCES""