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

Andreas Cap

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

Differential Geometry 2026-07-12 v1 Numerical Analysis

Authors: Andreas Cap

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 Schr\"odinger 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.

Keywords

BGG complexes differential forms representation theory semisimple Lie groups semisimple Lie algebras lecture notes

Cite

@article{arxiv.2607.10662,
  title  = {The Bernstein-Gelfand-Gelfand (BGG) Construction: Algebra, Geometry, and Analysis; Part I},
  author = {Andreas Cap},
  journal= {arXiv preprint arXiv:2607.10662},
  year   = {2026}
}

Comments

32 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;