Book Review: Theory of group representations

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

Book Review: Contemporary Sensorimotor Theory

Consciousness, with its irreducible subjective character, was almost exclusively a philosophical topic until relatively recently. Today, however, the problem of explaining the felt quality of experience has also become relevant to science and engineering, including robotics andAI: “What would we have to build into a robot so that it really felt the touch of a finger, the redness of red, or the ...

Group Representations and Character Theory

In this paper, we provide an introduction to the representation theory of finite groups. We begin by defining representations, G-linear maps, and other essential concepts before moving quickly towards initial results on irreducibility and Schur’s Lemma. We then consider characters, class functions, and show that the character of a representation uniquely determines it up to isomorphism. Orthogo...

QUASI-PERMUTATION REPRESENTATIONS OF SUZtTKI GROUP

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...

Elements of Finite Model Theory [book review]