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...

Each homogeneous space of a quasigroup affords a representation of the BoseMesner algebra of the association scheme given by the action of the multiplication group. The homogeneous space is said to be faithful if the corresponding representation of the Bose-Mesner algebra is faithful. In the group case, this definition agrees with the usual concept of faithfulness for transitive permutation rep...

We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced in [KLS08]. We generalize the central extension theorem of Buhler and Reichstein, [BR97, Theorem 5.3] and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev [KM08] about the essential dimen...

We show that a reductive group scheme over base S admits faithful linear representation if and only its radical torus is isotrivial, is, it splits after finite etale cover.

The human visual system possesses an impressive ability to remember and recognize complex three-dimensional shapes. The nature of the internal representations that underlie this ability, and the degree to which they mirror geometrical reality, are controversial 1, 2, 3]. According to some theories, the computational basis for shape representation is faithful encoding of structural 4] or metric ...