Pythagorean representations of Thompson's groups

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...

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 fai...

Representations of Finite Groups

Representations of braid groups

In this paper we survey some work on representations of Bn given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representation, recently came to prominence when it was shown to be faithful for all n. We will outline the methods used, applying them to a closely related representation for which the proof is slightly easier. The main tool is the...

Representations of Symmetric Groups

A surprising theorem in the modular representation theory of symmetric groups uses induction and restriction functors to define an action of an affine Kac-Moody special linear algebra on the level of Grothendieck groups. This action identifies the direct sum of Grothendieck groups with an integrable highest weight module of the Kac-Moody algebra. The purpose of this write-up is to provide a gen...