Groups, Geometries and Representation Theory
Title | 4P14b, Groups, Geometries and Representation Theory |
Term | Spring Term, 2013 |
Time | Wednesdays, 12pm-1pm, Thursdays 12pm-1pm |
Location | Watson B7 |
Prerequisites | 3P08a |
Lecture Notes | 42 pages, PDF |
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. |