Displaying similar documents to “Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties”

Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Frank Sottile (1999)

Colloquium Mathematicae

Similarity:

We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.

Geometry of third order ODE systems

Alexandr Medvedev (2010)

Archivum Mathematicum

Similarity:

We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application. ...