Fields Related to Brauer Characters.
Filtrations of the modules for Chevalley groups arising from admissible lattices.
Filtrations, Stable Clifford Theory and Group-Graded Rings and Modules.
Finite groups of OTP projective representation type
Let K be a field of characteristic p > 0, K* the multiplicative group of K and a finite group, where is a p-group and B is a p’-group. Denote by a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable -module is isomorphic to the outer tensor product V W of an indecomposable -module V and a simple...
Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic
Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and a finite group, where is a p-group and B is a p’-group. Denote by the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable...
Finite-dimensional twisted group algebras of semi-wild representation type
Let G be a finite group, K a field of characteristic p > 0, and the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.
Foncteurs de division et structure de dans la catégorie
Nous démontrons que dans la catégorie des foncteurs entre espaces vectoriels sur , le produit tensoriel entre le second foncteur injectif standard non constant et un foncteur puissance extérieure est artinien. Seul était antérieurement connu le caractère artinien de cet injectif ; notre résultat constitue une étape pour l’étude du troisième foncteur injectif standard non constant de .Nous utilisons le foncteur de division par le foncteur identité et des considérations issues de la théorie...
Frobenius symbols for partitions and degrees of spin characters.
Functor categories and group representations
G-algebras, Jacobson radical and almost split sequences.
Generalized support varieties for finite group schemes.
Generic representations of orthogonal groups: projective functors in the category
We continue the study of the category of functors , 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 ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in : and . As an application of these two decompositions, we give a complete description of the polynomial functors...
G-invariant quadratic forms.
Graded blocks of group algebras with dihedral defect groups
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.
Group Extensions and Splitting Modules.
Group representations without groups.
Group rings, Hecke orders, quasi-hereditary orders, cellular orders and deformations.
Groups with a Steinberg Character.
Harish-Chandra vertices.
Heights of spin characters in characteristic 2.