On normality of cones over symmetric varieties

Projective Normality of Complete Symmetric Varieties

We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety X = G/H is a surjective map. As a consequence the cone defined by a complete linear system over X, or over a closed G stable subvariety of X is normal. This gives an affirmative answer to a question raised by Faltings in [7]. A crucial point of the proof is a combinatoria...

Exact duality for optimization over symmetric cones

We present a strong duality theory for optimization problems over symmetric cones without assuming any constraint qualification. We show important complexity implications of the result to semidefinite and second order conic optimization. The result is an application of Borwein and Wolkowicz’s facial reduction procedure to express the minimal cone. We use Pataki’s simplified analysis and provide...

Normality of Nilpotent Varieties

We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.

Spherical Functions on Symmetric Cones

In this note, we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real Jordan algebra. We use this formula as an inspiration for a similar recursive formula involving the Jack polynomials.

Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties