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

Christine Vespa. "Generic representations of orthogonal groups: projective functors in the category $ℱ_{quad}$." Fundamenta Mathematicae 200.3 (2008): 243-278. <http://eudml.org/doc/286477>.

@article{ChristineVespa2008,
abstract = {We continue the study of the category of functors $ℱ_\{quad\}$, associated to ₂-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 $ℱ_\{quad\}$.},
author = {Christine Vespa},
journal = {Fundamenta Mathematicae},
keywords = {functor categories; quadratic forms; Mackey functors},
language = {eng},
number = {3},
pages = {243-278},
title = {Generic representations of orthogonal groups: projective functors in the category $ℱ_\{quad\}$},
url = {http://eudml.org/doc/286477},
volume = {200},
year = {2008},
}

TY - JOUR
AU - Christine Vespa
TI - Generic representations of orthogonal groups: projective functors in the category $ℱ_{quad}$
JO - Fundamenta Mathematicae
PY - 2008
VL - 200
IS - 3
SP - 243
EP - 278
AB - We continue the study of the category of functors $ℱ_{quad}$, associated to ₂-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 $ℱ_{quad}$.
LA - eng
KW - functor categories; quadratic forms; Mackey functors
UR - http://eudml.org/doc/286477
ER -