Representations of Hecke algebras at roots of unity
We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group , the derived and the stable categories of representations of a subgroup can be constructed out of the corresponding category for by a purely triangulated-categorical construction, analogous to étale extension in algebraic geometry. In the case of finite groups, we then use descent methods to investigate...
Nous étudions la cohomologie de la compactification des variétés de Deligne-Lusztig associées aux éléments de Coxeter. Nous présentons une conjecture des relations entre la cohomologie de la variété et la cohomologie de ses compactifications partielles. Nous prouvons la conjecture dans le cas du groupe linéaire général.
In this paper we get some properties which are compatible with the outer tensor product of local interior G-algebras in Section 2, in Section 3 we generalize the results of Külshammer in [2] on some indecomposable modules by the tool of inner tensor product of local interior G-algebras, we also discussed the centralizer CA(AG) of AG in A for an interior G-algebra A in Section 4, which makes sense for the extended definition in Section 1.
In this paper we calculate the 3-modular character table of the twisted Chevalley group 2D4(2) and its automorphism group 2D4(2).2. The Meat-Axe package for calculating modular characters over finite fields (Ryba (1990)) was used to calculate most of the characters. The method of condensation, which was explained in Suleiman (1990) was used to determine the complete character table. All these methods are explained later in this paper.