Timeline for McKay conjecture for finite groups in the simplest case G=GL(2,F_p) ( puzzle: Borel knows about cuspidals)
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2019 at 6:49 | vote | accept | Alexander Chervov | ||
| Jun 17, 2019 at 15:47 | answer | added | Geoff Robinson | timeline score: 7 | |
| Jul 9, 2017 at 19:27 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Jul 6, 2017 at 20:39 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Jul 6, 2017 at 20:32 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Jul 6, 2017 at 20:25 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Jul 6, 2017 at 19:01 | comment | added | Alexander Chervov | @JesseSilliman can you extend your comment to an answer - even if it is not complete it would be quite useful. | |
| Jul 6, 2017 at 16:05 | comment | added | Jesse Silliman | I can describe how the correspondence works for $GL_2(\mathbb{F}_p)$. One direction is given by restriction (and throwing away projective summands), the other by induction (and throwing away projective summands), I think that the irregular principal series have projective reductions mod p, so are not part of the Green Correspondence, while all the other irreducibles have, for some choice of integral structure, non-projective indecomposable reductions. I learned of the Green Correspondence from web.stanford.edu/~tonyfeng/mod_rep_theory.pdf | |
| Jul 6, 2017 at 7:28 | comment | added | Alexander Chervov | @JesseSilliman thank you for your comment ! Can you give reference and more info on "Green Correspondence" ? | |
| Jul 6, 2017 at 7:26 | comment | added | Alexander Chervov | @paulgarrett McKay predicts that characters of STANDARD torus gives both cuspidal and non. Can Weil&K rep be related to character of standard torus ? | |
| Jul 6, 2017 at 0:06 | comment | added | Jesse Silliman | The Green Correspondence in modular representation theory might also be relevant: it says that there is a bijection between the non-projective indecomposable mod p representations of $GL_2(\mathbb{F}_p)$ and those of $B(\mathbb{F}_p)$. | |
| Jul 5, 2017 at 22:17 | comment | added | paul garrett | For $SL_2(\mathbb F_q)$, the Segal-Shale-Weil/theta/Howe correspondence or pairing with the split $O(2)$ over $\mathbb F_q$ and also the non-split $O(2)$ do parametrize both (irreducible) principal series and cuspidal repns. Is this the sort of thing you'd be interested in? | |
| Jul 5, 2017 at 19:51 | history | edited | YCor | CC BY-SA 3.0 |
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| Jul 5, 2017 at 19:37 | history | edited | Alexander Chervov | CC BY-SA 3.0 |
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| Jul 5, 2017 at 19:29 | history | asked | Alexander Chervov | CC BY-SA 3.0 |