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Generic representations of orthogonal groups: projective functors in the category q u a d

Christine Vespa (2008)

Fundamenta Mathematicae

We continue the study of the category of functors q u a d , 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 q u a d ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in q u a d : P H and P H . As an application of these two decompositions, we give a complete description of the polynomial functors...

Graded blocks of group algebras with dihedral defect groups

Dusko Bogdanic (2011)

Colloquium Mathematicae

We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.

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