Representations of infinite soluble groups

Infinite-dimensional Representations of Real Reductive Groups

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...

Infinite Dimensional Groups, Their Representations, Orbits, Invariants

1. Representation theory for infinite dimensional groups does not exist as a theory although such groups occur long ago in several branches of mathematics and its applications. Among the most important examples are: (a) groups of automorphisms of infinite dimensional vector spaces with some additional structures (unitary, symplectic, Fredholm etc.); (b) groups of diffeomorpliisms of smooth mani...

QUASI-PERMUTATION REPRESENTATIONS OF METACYCLIC 2-GROUPS

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras

Linear representations of soluble groups of finite Morley rank

Sufficient conditions are given for groups of finite Morley rank having non-trivial torsion-free nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsion-free Fitting subgroups have faithful linear representations. On the way, using a notion of definable weight space, we prove that certain...