Abstract.
For a connected reductive group G and a Borel subgroup B, we study the closures of double classes BgB in a \( (G \times G) \)-equivariant "regular" compactification of G. We show that these closures \( \overline {BgB} \) intersect properly all \( (G \times G) \)-orbits, with multiplicity one, and we describe the intersections. Moreover, we show that almost all \( \overline {BgB} \) 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.
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Received: June 23, 1997
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Brion, M. The behaviour at infinity of the Bruhat decomposition. Comment. Math. Helv. 73, 137–174 (1998). https://doi.org/10.1007/s000140050049
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DOI: https://doi.org/10.1007/s000140050049