The Bernstein-Gelfand-Gelfand (BGG) Construction: Algebra, Geometry, and Analysis; Part I

Abstract

These are lecture notes for the first part of a short course that I taught jointly with Kaibo Hu as part of the thematic program "Differential Complexes: Theory, Discretization, and Applications" at the Erwin Schrödinger Institute (ESI) in Vienna. We give an introduction to differential forms and the construction of Berstein-Gelfand-Gelfand (BGG) complexes on open domains in R^n, focusing on the role of representation theory of semisimple Lie groups and Lie algebras in the construction.

arXiv comment32 pages. Videos of the lectures are available via the youtube channel of the ESI; I do not intend to publish these notes, they are posted for reference purposes only;