Induced representation

Abstract: Notation Background from Group Theory Representations and Modules Algebraic Number Theory Semi-Simple Rings and Group Algebras Group Characters Induced Characters Induced Representation Non-Semi-Simple Rings Frobenius Algebras Splitting Fields and Separable Algebras Integral Representations Modular Representations Index

Abstract: Representations and characters: generalities on linear representations character theory subgroups, products, induced representation compact groups examples. Representations in characteristic zero: the group algebra induced representations Mackey's criterion examples of induced representations Artin's theorem a theorem of Brauer applications of Brauer's theorem rationality questions - examples. Introduction to Brauer theory: the groups RK(G), RX(G) and PK(G) the cde triangle theorems proofs modular characters application to Artin representations.

Abstract: A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.

Abstract: We construct projective unitary representations of (a) Map(S1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that a class of representations of Map(S1;T), whereT is a maximal torus ofG, can be extended to representations of Map(S1;G),