Groups, Geometries and Representation Theory

This course develops the ordinary, and partly modular, representation theory of symetric groups.

The syllabus is as follows.

Partitions, tableaux, tabloids and polytabloids;

Dominance lemma for partitions and tabloids;

Young subgroups. Robinson--Schensted(-Knuth) algorithm;

The abacus;

Construction of Sλ and Mλ;

James's submodule theorem;

The Specht modules form a complete set of irreducible Sn-modules;

Definition of Dλ and that they form a complete set of irreducible Sn-modules over a field of characteristic p;

Branching rule;

Young's rule;

Littlewood--Richardson rule;

Murnaghan--Nakayama rule.