In analogy with transition equations for type Schubert polynomials given by Lascou and Schutzenberger s 14 , we give recursive formulas for computing representatives of the Schubert classes for the isotropic ag manifolds. These representatives are e actly the Schubert polynomials found in 2 . This new approach to nding Schubert polynomials is very closely related to the geometry of the ag manif...

We present a formal, algebraic treatment of Fedosov’s argument that the coordinate algebra of a symplectic manifold has a deformation quantization. His remarkable formulas are established in the context of affine symplectic algebras.

A strict quantization of a Poisson manifold P on a subset

In the framework of C-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes’ tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel’s noncommutative torus, and even Landi’s noncommutative 4-sphere. We construct such groupoid for a wide class of T-spaces, that generalizes the one given for C by ...

Let G be a 1-connected, almost-simple Lie group over a local field and S a subsemigroup of G with non-empty interior. The action of the regular hyperbolic elements in the interior of S on the flag manifold G/P and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the contr...

In this paper, we give a new formulation of invariant theory for elliptic Weyl group using the group O(2, n). As an elliptic Weyl group quotient, we define a suitable C∗-bundle. We show that it has a conformal Frobenius structure which we define in this paper. Then its good section could be identified with a Frobenius manifold which we constructed in [13].

It is proved that any compact almost Kähler, Einstein 4-manifold whose fundamental form is a root of the Weyl tensor is necessarily Kähler.