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Description: |
We present the general problem of constructing geometric
quotients and orbit spaces. The study of simultaneous
conjugation of several complex m by m matrices can be viewed
as a particular instance of this problem, and in this case
the generic orbits have well-known descriptions.
The case of 2 by 2 matrices is particularly simple, and one
can find invariants for all orbits, including the
non-generic ones. A very simple explicit criterium for the
simultaneous triangularization of 2 by 2 matrices is
described. We also obtain corresponding results for the
variety of GL(2,C)-characters of a finitely generated group.
Area(s):
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