Fubini-Griffiths-Harris rigidity and lie algebra cohomology

Journal Article (Journal Article)

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 ℙg) is extrinsically rigid to third order (with the exception of g = a1). In contrast, we show that the adjoint variety of SL3ℂ and the Segre product Seg(ℙ1 × ℙn) are flexible at order two. In the SL3ℂ 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.

Full Text

Duke Authors

Cited Authors

  • Landsberg, JM; Robles, C

Published Date

  • January 1, 2012

Published In

Volume / Issue

  • 16 / 4

Start / End Page

  • 561 - 586

Electronic International Standard Serial Number (EISSN)

  • 1945-0036

International Standard Serial Number (ISSN)

  • 1093-6106

Digital Object Identifier (DOI)

  • 10.4310/AJM.2012.v16.n4.a1

Citation Source

  • Scopus