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Reischuk, Rebecca: The monoidal structure on strict polynomial functors. 2016
Inhalt
Introduction
Motivation and Main Results
Outline
Notations and Prerequisites
Strict Polynomial Functors
Prerequisites
The Category of Divided Powers
The Category of Strict Polynomial Functors
Morphisms Between Strict Polynomial Functors
Monoidal Structure
Highest Weight Structure
Dualities
Representations of the Symmetric Group
Monoidal Structure
Permutation Modules
Cellular Structure
The Schur Functor
The Adjoints of the Schur Functor
The Left Adjoint of the Schur Functor
The Right Adjoint of the Schur Functor
Both Adjoints
The Tensor Product on Strict Polynomial Functors
Divided, Symmetric and Exterior Powers
Schur and Weyl Functors
Simple Functors
Modules over the Schur Algebra
Projective Objects
Monoidal Structure
Highest Weight Structure
Duality
The Schur Functor
Conclusion
Appendix
Standard Morphisms
The Multiplication Rule for Schur Algebras
Correspondence Between Objects and Morphisms
Glossary
Bibliography