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European Mathematical Society Publishing House
2016-09-19 17:04:49
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
73
1998
1
The behaviour at infinity of the Bruhat decomposition
Michel
Brion
Université Grenoble I, SAINT MARTIN D'HERES CEDEX, FRANCE
Bruhat decomposition, regular embedding, Chow ring
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.
Group theory and generalizations
General
137
174
10.1007/s000140050049
http://www.ems-ph.org/doi/10.1007/s000140050049