Can I recognize the quotient of a group by a closed subgroup? (for example the standard representation of S3 in GL(2,C)) - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T10:06:26Z http://mathoverflow.net/feeds/question/71771 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/71771/can-i-recognize-the-quotient-of-a-group-by-a-closed-subgroup-for-example-the-st Can I recognize the quotient of a group by a closed subgroup? (for example the standard representation of S3 in GL(2,C)) Yosemite Sam 2011-08-01T00:04:07Z 2011-08-01T00:04:07Z <p>The first question might be too much in general.</p> <p>The cases I'd like to understand in practice are quotients (as algebraic varieties) of GL(n,C) (or SL(n,C) if you prefer) by finite subgroups. Is there anything I can say about the quotient (set of cosets)?</p> <p>The babiest case would be the standard rep of the dihedral/symmetric group \$S_3\$. What is \$GL(2,C)/S_3\$? Or \$SL(2,C)/S_3\$ if it makes things easier?</p> <p>Essentially what I'm trying to do is embed a finite group in a special group (in the technical sense) and understanding what the quotient is.</p> <p>Any ideas or references?</p>