On intersections of certain partitions of a group compactification

Xuhua He Jiang-Hua Lu

Representation Theory mathscidoc:1912.43222

International Mathematics Research Notices, 2011, (11), 2534-2564, 2011
Let G be a connected semi-simple algebraic group of adjoint type over an algebraically closed field and let ar G be the wonderful compactification of G. For a fixed pair (B,B <sup></sup> ) of opposite Borel subgroups of G, we look at intersections of Lusztigs G-stable pieces and the B <sup></sup> B-orbits in ar G , as well as intersections of BB-orbits and B <sup></sup> B <sup></sup> -orbits in ar G . We give explicit conditions for such intersections to be nonempty, and in each case, we show that every nonempty intersection is smooth and irreducible, that the closure of the intersection is equal to the intersection of the closures, and that the nonempty intersections form a strongly admissible partition of .
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  title={On intersections of certain partitions of a group compactification},
  author={Xuhua He, and Jiang-Hua Lu},
  booktitle={International Mathematics Research Notices},
Xuhua He, and Jiang-Hua Lu. On intersections of certain partitions of a group compactification. 2011. Vol. 2011. In International Mathematics Research Notices. pp.2534-2564. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113031033351782.
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