Standard Monomial Theory for Wonderful Varieties

Standard Monomial Theory

We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Zi associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties. In this paper, we prove the results announced in [LkMg] for the case of Type An−1 (the groups GL(n) and SL(n)). ...

Automorphisms of Wonderful Varieties

Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut(X) and we calculate Luna’s invariants of X under its action.

Standard Monomial Theory for Harmonics in Classical Invariant Theory

A Geometric Approach to Standard Monomial Theory

We obtain a geometric construction of a “standard monomial basis” for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert varieties, opposite Schubert varieties, and unions of intersections of these varieties. Our approach relies on vanishing theorems and a degeneration of the diagonal; it also yields a standard monom...

Wonderful Varieties of Type E

The classification of spherical varieties is already known for semisimple groups of types A and D. Adding type E, we complete the classification for all semisimple groups with a simply laced Dynkin diagram.