Let G be a reductive group acting on an affine variety X , and let x ∈ X be a point whose G-orbit is not closed. In this paper, we study G.R. Kempf’s optimal class of cocharacters of G attached to the point x; in particular, we consider how this optimality transfers to subgroups of G. Our main result says that if K is a G-completely reducible subgroup of G which fixes x, then the optimal class ...

We compute the sequence of colengths in the cocharacters of the ∗polynomial identities of the ∗-simple algebra M2(F )⊕M2(F ), char(F ) = 0.

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we consider particular classes of connected reductive subgroups H of G and show that the cocharacters of H that are associated to a given nilpotent element e in the Lie algebra of H are precisely the cocharacters of G associated to e tha...

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper we prove that if T W̃ is the toric arrangement defined by the cocharacters lattice of a Weyl group W̃ , then the integer cohomology of its complement is torsion free.

Introduction 967 1. Reductive groups and p-divisible groups 971 (1.1) Cocharacters and filtrations 971 (1.2) Review of S-modules 973 (1.3) Reductive groups and crystalline representations 975 (1.4) Application to p-divisible groups 978 (1.5) Deformation theory 981 2. Integral canonical models of Hodge type 986 (2.1) Shimura varieties 986 (2.2) Absolute Hodge cycles 989 (2.3) Integral models 992...

we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.