Geometric representations of GL(n,R), cellular Hecke algebras and the embedding problem

We study geometric representations of GL(n,R) for a ring R. The structure of the associated Hecke algebras is analyzed and shown to be cellular. Multiplicities of the irreducible constituents of these representations are linked to the embedding problem of pairs of R-modules x < y.Comment: 18 pages, final version, to appear in JPA

Algebraic Representations of Ergodic Actions and Super-Rigidity

We revisit Margulis-Zimmer Super-Rigidity and provide some generalizations. In particular we obtain super-rigidity results for lattices in higher-rank groups or product of groups, targeting at algebraic groups over arbitrary fields with absolute values. We also obtain cocycle super-rigidity results for a wide class of groups with respect to mixing actions. Our approach is based on a systematic study of algebraic representations of ergodic actions.Comment: 25 pages. The file is different from a previously distributed file by the same name. 2nd submission: an inaccuracy in the definition of a morphism of bi-algebraic representations was fixe