137,152 research outputs found
Convergence and limits of linear representations of finite groups
Motivated by the theory of graph limits, we introduce and study the
convergence and limits of linear representations of finite groups over finite
fields. The limit objects are infinite dimensional representations of free
groups in continuous algebras. We show that under a certain integrality
condition, the algebras above are skew fields. Our main result is the extension
of Schramm's characterization of hyperfiniteness to linear representations.Comment: Final version. To appear in the Journal of Algebr
L^2-Betti numbers and Plancherel measure
We compute -Betti numbers of postliminal, locally compact, unimodular
groups in terms of ordinary dimensions of reduced cohomology with coefficients
in irreducible unitary representations and the Plancherel measure. This allows
us to compute the -Betti numbers for semi-simple Lie groups with finite
center, simple algebraic groups over local fields, and automorphism groups of
locally finite trees acting transitively on the boundary.Comment: 11 page
- …