Fubini-Griffiths-Harris rigidity and Lie algebra cohomology Academic Article uri icon


  • We prove a rigidity theorem for represented semi-simple Lie groups. The theorem is used to show that the adjoint variety of a complex simple Lie algebra g (the unique minimal G orbit in g) is extrinsically rigid to third order (with the exception of g = a1). In contrast, we show that the adjoint variety of SL3 and the Segre product Seg(1 n) are flexible at order two. In the SL3 example we discuss the relationship between the extrinsic projective geometry and the intrinsic path geometry. We extend machinery developed by Hwang and Yamaguchi, Se-ashi, Tanaka and others to reduce the proof of the general theorem to a Lie algebra cohomology calculation. The proofs of the flexibility statements use exterior differential systems techniques. 2012 International Press.

published proceedings

  • Asian Journal of Mathematics

author list (cited authors)

  • Landsberg, J. M., & Robles, C.

citation count

  • 4

complete list of authors

  • Landsberg, Joseph M||Robles, Colleen

publication date

  • January 2012