Orbits of a maximal torus on a flag space
Let G be a semisimple complex group, B be a Borel subgroup, X be the closure in G/B of a general orbit of a maximal torus. The author describes a basis of the homologies \(H_*(X,{\mathbb{Z}})\) and the image of the restriction homomorphism \(i^*: H^*(G/B,{\mathbb{Q}})\to H^*(X,{\mathbb{Q}})\). This image is the algebra of invariants \(H(X,{\mathbb{Q}})^ W\) with respect of the action induced by an action of the Weyl group W on X. There is an explicit presentation of generators and defining relations for this algebra of invariants. The \(i^*\)-images of the generalized Schubert cocycles are expressed in the terms of these generators. The note contains some applications to the case \(G=GL_ n\) and to usual Schubert cells.
orbits of a maximal torus on a flag space
scientific article; zbMATH DE number 3929181