Search results with tag "Representation theory"
Introduction to representation theory
math.mit.eduTypical problems of representation theory are as follows: 1. Classify irreducible representations of a given algebra A. 2. Classify indecomposable representations of A. 3. Do 1 and 2 restricting to finite dimensional representations. As mentioned above, the algebra A is often given to us by generators and relations. For
Introduction to representation theory
www-math.mit.edumade the following observation: take the multiplication table of a finite group Gand turn it into a matrix X G by replacing every entry gof this table by a variable x g . Then the determinant of X G
Representation Theory - James Lingard - Home Page
www.jchl.co.ukWe say that a representation is indecomposible if it is not a direct sum of smaller representations. If V is indecomposible then it is irreducible, but the converse does not follow in general. Permutation representations Let G act on a set X.Then the permutation representation of G with respect to this action, k[X], is a jXj-dimensional vector space over k with basis fex jx 2 Xg.