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.net2013-05-23T10:06:26Zhttp://mathoverflow.net/feeds/question/71771http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/71771/can-i-recognize-the-quotient-of-a-group-by-a-closed-subgroup-for-example-the-stCan I recognize the quotient of a group by a closed subgroup? (for example the standard representation of S3 in GL(2,C))Yosemite Sam2011-08-01T00:04:07Z2011-08-01T00:04:07Z
<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>