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Mar 28, 2020 at 21:04 history edited paul garrett CC BY-SA 4.0
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Mar 27, 2020 at 21:09 comment added paul garrett Maps to Fourier-Whittaker or Fourier-Jacobi or Fourier-Bessel or whatever components are $G$-homs, so preserve all $G$-related properties. Averaging on the left, etc., is a $G$-hom for the right action of $G$. This is mostly disjoint from the restriction-to-subgroup maps, which are not-so-often given by integration along some sort of "complementary subgroup".
Mar 27, 2020 at 20:49 vote accept Monty
Mar 27, 2020 at 20:04 history answered paul garrett CC BY-SA 4.0