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Aug 14, 2014 at 21:44 history edited Roman CC BY-SA 3.0
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Aug 14, 2014 at 17:29 comment added Alexander Braverman Actually I don't understand why the center of $Mp(2)$ acts non-trivially in this representation.
Aug 14, 2014 at 16:13 history edited Roman CC BY-SA 3.0
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Aug 14, 2014 at 16:04 comment added Roman Mp(2) acts on functions and hence on distributions on $K^4=gl(2)$ (as well as $K^3=sl(2)$). In fact a bigger group Mp(8) (resp. Mp(6)) acts there (and its central element surely acts but a nontrivial scalar), then the quadratic form $det$ defines a homomorphism $Mp(2)\to Mp(8)$.
Aug 14, 2014 at 15:09 comment added Alexander Braverman Below Semyon claims that there is a distribution on degenerate matrices whose FT is concentrated there as well, but so far I don't understand all the details.
Aug 14, 2014 at 15:02 comment added Alexander Braverman I didn't understand the last argument - on what space does the group Mp(2) act?
Aug 14, 2014 at 14:46 history answered Roman CC BY-SA 3.0