Cohomological Tensor Functors on Representations of the General Linear Supergroup

• Record Nr.: UNINA9910957044903321
• Autore: Heidersdorf Thorsten
• Pubbl/distr/stampa: Providence : , : American Mathematical Society, , 2021; ©2021
• ISBN: 9781470465285; 1470465280
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (118 pages)
• Collana: Memoirs of the American Mathematical Society ; ; v.270
• Classificazione: 17B1017B2017B5518D1020G05
• Altri autori (Persone): WeissauerRainer
• Disciplina: 512/.57
• Soggetti: Tensor algebra; Tensor products; Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Representations, algebraic theory (weights); Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Simple, semisimple, reductive (super)algebras; Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Homological methods in Lie (super)algebras; Category theory; homological algebra -- Categories with structure -- Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories; Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Cohomological Tensor Functors -- 2.1. The superlinear groups -- 2.2. The Duflo-Serganova functor -- 2.3. Cohomology functors -- 2.4. Support varieties and the kernel of -- 2.5. The tensor functor -- 2.6. The relation between ( ) and ( ) -- 2.7. Hodge decomposition -- 2.8. The case &gt -- 1 -- 2.9. Boundary maps -- 2.10. Highest weight modules -- 2.11. The Casimir -- Chapter 3. The Main Theorem and its Proof -- 3.1. The language of Brundan and Stroppel -- 3.2. On segments, sectors and plots -- 3.3. Mixed tensors and ground states -- 3.4. Sign normalizations -- 3.5. The main theorem -- 3.6. Strategy ; of the proof -- 3.7. Modules of Loewy length 3 -- 3.8. Inductive Control over -- 3.9. Moves -- Chapter 4. Consequences of the Main Theorem -- 4.1. Tannaka Duals -- 4.2. Cohomology I -- 4.3. Cohomology II -- 4.4. Cohomology III -- 4.5. The forest formula -- 4.6. -module structure on the cohomology ^{∙}_{ _{ }} -- 4.7. Primitive elements of ^{∙}_{ _{ }}( (1)) -- 4.8. Kac module of 1 -- 4.9. Strict morphisms -- 4.10. The module (( )ⁿ) -- 4.11. The basic hook representations -- Bibliography -- Back Cover.
• Sommario/riassunto: "We define and study cohomological tensor functors from the category Tn of finite-dimensional representations of the supergroup for the image of an arbitrary irreducible representation. In particular DS(L) is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation"--