The BGG complex on projective space
The article is related to differential calculus on real or complex projective space invariant with respect to projective transformations forming a semisimple Lie group. The Bernstein-Gelfand-Gelfand (BGG) complexes on \(\mathbb{RP}_n\) or \(\mathbb{CP}_n\) are complexes of vector bundles and differential operators between them the generalizing de Rham complex on \(\mathbb{RP}_n\) and the holomorphic de Rham complex on \(\mathbb{CP}_n\) respectively. Here, employing the projective invariance, the authors derive explicit formulae for the operators in the projective BGG complex on \(\mathbb{RP}_n\) in terms of the usual round metric on the sphere \(S^n\) as its double cover.
Bernstein-Gelfand-Gelfand (BGG) complexes
scientific article; zbMATH DE number 6050679