Representation Theory , Lecture 0

Lecture 21

1 Overview In this lecture, we will • Wrap up Alon-Edmonds-Luby's graph theoretical codes: construction and analysis of distance • Introduce the interplay between codes and computational complexity: open problems and pseudorandomness 2 Alon-Edmonds-Luby The construction of the code depends on three main ingredients: • A binary code C 0 = [d, R 0 d, δ 0 d] 2 , where R 0 and δ 0 are our target ra...

LECTURE 15: REPRESENTATIONS OF Uq(g) AT ROOTS OF 1

In Lecture 13 we have studied the representation theory of Uq(g) when q is not a root of 1. We have seen that the representation theory basically looks like the representation theory of g (over C). In this lecture we are going to study a more complicated case: when q is a root of 1 (we still need to exclude some small roots of 1 to make the algebra Uq(g) defined). When we deal with the usual de...

Lecture 1: Representations of Symmetric Groups, I

In this lecture we start to study the representation theory of the symmetric groups Sn over C. Let us summarize a few things that we already know. 0) A representation of Sn is the same thing as a representation of the group algebra CSn. 1) As with all finite groups, any representation of Sn over C is completely reducible. 2) The number of irreducible representations of Sn coincides with the num...

Lecture Notes Spring 2006 M 690 I : Extremal Graph Theory

MATH5735 Modules and Representation Theory Lecture Notes