JournalscmhVol. 73, No. 1pp. 137–174

The behaviour at infinity of the Bruhat decomposition

  • Michel Brion

    Université Grenoble I, Saint-Martin-d'Hères, France
The behaviour at infinity of the Bruhat decomposition cover

Abstract

For a connected reductive group G and a Borel subgroup B, we study the closures of double classes BgB in a (G×G)(G \times G) -equivariant "regular" compactification of G. We show that these closures BgB\overline {BgB} intersect properly all (G×G)(G \times G) -orbits, with multiplicity one, and we describe the intersections. Moreover, we show that almost all BgB\overline {BgB} 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. 137–174

DOI 10.1007/S000140050049