Dominique Luna

"On Demazure embeddings"

Let G be a complex reductive group, and let H be a Spherical subgroup of G which is equal to its normalizer. The closure of G.LieH in The grassmannian of LieG of subspaces of dimension dim(LieH) , is called the Demazure embedding of G/H . When H is a symmetric subgroup, De Concini and Procesi proved in 1983 that Demazure embeddings are wonderful (i.e. they are smooth and projective; the complement of G.LieH is a union of smooth irreducible G-invariant divisors which have a transversal and non empty intersection; and any two points which are contained in the same G-invariant divisors, are on the same G-orbit). In the general spherical case, it follows from results of Brion and Knop, that Demazure embeddings are wonderful whenever they are normal. In my talk, I will show that normality fails sometimes, and when G is of type A, I will determine all G/H having wonderful Demazure embeddings.