Representation Theory and Projective Geometry

By J. M. Landsberg, Laurent Manivel. 2002

50 citations recorded by the source corpus.

This article consists of three parts that are largely independent of one another. The first part deals with the projective geometry of homogeneous varieties, in particular their secant and tangential varieties. It culminates with an elementary construction of the compact Hermitian symmetric spaces and the closed orbits in the projectivization of the adjoint representation of a simple Lie algebra. The second part discusses division algebras, triality, Jordan agebras and the Freudenthal magic square. The third part describes work of Deligne and Vogel inspired by knot theory and several perspectives for understanding this work.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/283eda3f76e24aee21cb84d2c6b657888f30d14a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Laurent Manivel
2. Alberto Elduque
3. Daniele Faenzi
4. J. M. Landsberg

In Mathematical Physics

1. Laurent Manivel
2. J. M. Landsberg

Citations in the corpus

• Configurations of lines and models of Lie algebras (2005, methodology): “Restricting the adjoint representation of spin8 to the corresponding subalgebra, a product of four copies of sl2, we obtain the four-ality model [ 28 ]”