For a connected reductive group G and a Borel subgroup B, we study the closures of double classes BgB in a -equivariant "regular" compactification of G. We show that these closures intersect properly all -orbits, with multiplicity one, and we describe the intersections. Moreover, we show that almost all are singular in codimension two exactly. We deduce this from more general results on B-orbits in a spherical homogeneous space G/H; they lead to formulas for homology classes of H-orbit closures in G/B, in terms of Schubert cycles.
Cite this article
Michel Brion, The behaviour at infinity of the Bruhat decomposition. Comment. Math. Helv. 73 (1998), no. 1, pp. 137–174DOI 10.1007/S000140050049