Timeline for $\DeclareMathOperator\SL{SL}$Multiplicities of irreducible representations in discrete part of $L^2(\SL(2,\mathbb{Z})\backslash{\SL(2,\mathbb R)})$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2022 at 21:02 | vote | accept | Jun Yang | ||
| Jan 8, 2022 at 10:07 | answer | added | GH from MO | timeline score: 4 | |
| Jan 8, 2022 at 2:40 | comment | added | Jun Yang | @PeterHumphries Thank you for the answer! Only for the real case (instead of the adelic one), what the most we can tell about the multiplicities $m_{\pi}$? | |
| Jan 8, 2022 at 2:34 | comment | added | Jun Yang | @paulgarrett I edited the question. Thank you! | |
| Jan 8, 2022 at 2:32 | history | edited | Jun Yang | CC BY-SA 4.0 |
added 366 characters in body
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| Jan 7, 2022 at 23:50 | comment | added | Kimball | Even after Peter's edit, I have no idea what the OP is asking. Please ask a specific, precise question. | |
| Jan 7, 2022 at 23:06 | comment | added | Peter Humphries | Are you asking whether these representations occur with multiplicity one? The space of modular forms of weight $k$ has dimension $\approx \frac{k}{12}$, so the discrete series representation of weight $k$ occurs with high multiplicity. For principal series representations, it is conjectured that the multiplicity is one (see e.g. cds.cern.ch/record/260472/files/P00022028.pdf). See also my answer here: mathoverflow.net/questions/320171/… | |
| Jan 7, 2022 at 23:01 | history | edited | Peter Humphries | CC BY-SA 4.0 |
added 39 characters in body; edited tags
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| Jan 7, 2022 at 22:34 | comment | added | paul garrett | There's some imprecision in the premises of your question: yes, the (holomorphic or antiholomorphic) discrete series occur exactly as holo or anti-holo cuspforms, but wavefore-cuspforms generate principal_series repns of $SL_2(\mathbb R)$. Possibly your premise was just a mis-statement? | |
| Jan 7, 2022 at 22:25 | comment | added | LSpice | Which 1975 Gelbart book? | |
| Jan 7, 2022 at 22:23 | history | edited | LSpice | CC BY-SA 4.0 |
`\DeclareMathOperator`
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| Jan 7, 2022 at 22:01 | history | asked | Jun Yang | CC BY-SA 4.0 |