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Aug 31, 2020 at 7:14 comment added Peter Humphries All done now! See arxiv.org/abs/2008.12406
Aug 17, 2020 at 17:43 vote accept user15243
May 16, 2020 at 13:25 history edited Peter Humphries CC BY-SA 4.0
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May 16, 2020 at 2:19 comment added Peter Humphries Sadly still developing (at least for $\operatorname{GL}_n(\mathbb{R})$; the proofs are complete for $\operatorname{GL}_n(\mathbb{C})$). The theory itself takes too much work to state in a comment, so I will just link to the Oberwolfach Report where I first announced the result: mfo.de/document/1736/OWR_2017_40.pdf (P.S. It's 4am - go back to sleep!)
May 16, 2020 at 2:02 comment added GH from MO @PeterHumphries: Thank you, Peter. Perhaps you can also mention somewhere the archimedean analogue you were developing. I am too busy now, e.g. I wrote the above answer in a rush!
May 15, 2020 at 23:52 comment added Peter Humphries Other useful references: this paper of Casselman for $\mathrm{GL}_2$: doi.org/10.1007/BF01428197. And another correct proof for $\mathrm{GL}_n$ due to Matringe: math.uni-bielefeld.de/documenta/vol-18/37.pdf
May 15, 2020 at 23:49 history edited LSpice CC BY-SA 4.0
Links to book
May 15, 2020 at 23:28 history answered GH from MO CC BY-SA 4.0