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May 14, 2021 at 22:44 comment added DamienC @MathManiac Yes, you're seeing through my argument correctly. It is true that the reduced system has less parameters, but it doesn't mean that it's simpler. Sometimes it becomes more complicated (and thus, more interesting).
May 13, 2021 at 22:13 comment added MathManiac @DamienC So, just to confirm that I’m seeing through your argument correctly, in the example that you mention here, symplectic reduction is a tool to understand the Calogero-Moser space better, because the equations in terms of matrices are simpler to understand and compute with, am I right? If yes, then this seems a bit strange to me, because I thought that the whole idea of reduction was to reduce the number of parameters to get a system which is supposedly simpler.
Mar 28, 2016 at 22:05 comment added DamienC $PGL_n$ acts (by simultaneous conjugation on both factors) .
Jan 21, 2016 at 9:20 comment added Olga Maybe I didn't get something? What group is acting in your matrix example and how?
May 5, 2011 at 15:14 history answered DamienC CC BY-SA 3.0