Lie algebras and their representations

Monday 13-15, Thursday 10-12, HG D1.2

Tentative programme:

Lie algebras, Lie groups --- The Campbell-Baker-Hausdorff formula --- Young diagrams and representations of gl(n), u(n) --- General Lie theory: theorems of Engel and Lie --- Semisimple Lie algebras --- Roots, weights and the Weyl group --- The universal enveloping algebra, Poincare'-Birkhoff-Witt theorem, Harish--Chandra homomorphism --- Verma modules, highest weight modules --- Weyl character formula --- (if time permits) Differential graded Lie algebras and Q-manifolds, introduction to deformation theory

Problem set 1, due 7 April

Problem set 2, due 21 April

Problem set 3, due 19 May

Problem set 4, due 2 June

Problem set 5, due 16 June

On 9 and 12 May the lectures will be given by Chenchang Zhu
The exercise session on 19 May will take place from 8.15 to 10 in HG G 46