More familiar description of wonderful compactification of SL_n/S(GL_2 \times GL_n-2) - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T01:46:11Z http://mathoverflow.net/feeds/question/100423 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100423/more-familiar-description-of-wonderful-compactification-of-sl-n-sgl-2-times-gl More familiar description of wonderful compactification of SL_n/S(GL_2 \times GL_n-2) Daniel Pomerleano 2012-06-23T03:34:40Z 2012-06-23T19:28:16Z <p>I am trying to learn a bit about spherical geometry and wonderful compactifications. Please correct any misconceptions. If I've understood <a href="http://www.springerlink.com/content/x62342v721707828/" rel="nofollow">http://www.springerlink.com/content/x62342v721707828/</a> properly, wonderful compactifications of rank one homogeneous spaces have more familiar descriptions. For example the wonderful compactification of $SO_n/SO_{n-1}$ is a quadric. I was wondering if the same might be true for some rank 2 homogeneous spaces such as:</p> <p>$SL_n/S(GL_2 \times GL_{n-2})$, where n is at least 4,</p> <p>Does the wonderful compactification of this variety show up outside of wonderful geometry at least for low n? If not is there a relatively simple algorithm to at least compute its cohomology? </p>