Generic representations of orthogonal groups: projective functors in the category $ℱ_{quad}$

• Autorzy: Christine Vespa
• Języki publikacji: EN

Abstrakty

EN

We continue the study of the category of functors $ℱ_{quad}$, associated to 𝔽₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in $ℱ_{quad}$; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in $ℱ_{quad}$: $P_{H₀}$ and $P_{H₁}$. As an application of these two decompositions, we give a complete description of the polynomial functors in $ℱ_{quad}$.

Kategorie tematyczne

• 20C20: Modular representations and characters
• 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
• 20J99: None of the above, but in this section
• 18A25: Functor categories, comma categories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 200
• Numer: 3
• Strony: 243-278

Daty

wydano

2008

Twórcy

autor

Christine Vespa

• Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg Cédex, France

Identyfikatory

DOI

10.4064/fm200-3-2