Timeline for Volume of a double class of a parahoric subgroup
Current License: CC BY-SA 4.0
18 events
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| Sep 14 at 12:45 | answer | added | Hodge-Tate | timeline score: 3 | |
| Sep 14 at 9:03 | comment | added | Paul Broussous | @Hodge-Tate Thank you very much for this reference! May be you should post it as an answer? | |
| Nov 14, 2018 at 17:03 | comment | added | Paul Broussous | @paulgarrett I made my question more precise. | |
| Nov 14, 2018 at 16:48 | comment | added | Paul Broussous | @LSpice Thanks, you're right. I made the correction. | |
| Nov 14, 2018 at 16:46 | history | edited | Paul Broussous | CC BY-SA 4.0 |
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| Nov 14, 2018 at 16:44 | history | edited | LSpice | CC BY-SA 4.0 |
Minor notation smoothing
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| Nov 14, 2018 at 16:41 | comment | added | LSpice | Also, in your last line, do you really mean to ask just for $\mu(P)$, or (as the rest of your question suggests) for $\mu(P w P)$ for a certain element $w$? | |
| Nov 14, 2018 at 16:40 | comment | added | LSpice | @paulgarrett, Casselman gives a distinguished choice of representatives for the double cosets you describe in Proposition 1.1.3 of the p-adic notes; for example, one can take the minimal-length elements in each coset. (I guess that doesn't make it terribly easy to count them.) | |
| Nov 14, 2018 at 16:21 | history | edited | Paul Broussous | CC BY-SA 4.0 |
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| Nov 14, 2018 at 16:21 | comment | added | Paul Broussous | @paulgarrett Indeed I'm looking for closed formulas in particular cases. | |
| Nov 13, 2018 at 22:54 | comment | added | paul garrett | ... but/and do you need more than that sort of pseudo-algorithmic description? | |
| Nov 13, 2018 at 22:50 | comment | added | paul garrett | I suppose you know as well as I that the cell multiplication rule(s), $BwB\cdot BsB = BwsB$ for length $ws$ greater than that of $w$, and with an addition term $\sqcup BwB$ when $ws$ is not longer, and the Bruhat decomposition of each $P$, give some sort of description of the volume/index. Likewise, I'd bet you know that $P\backslash G/Q\approx W_P\backslash W/W_Q$ for "parabolics/parahorics" $P,Q$, so the issue of systematic description partly devolves into existence of a "nice" choice of reps for $W_P\backslash W/W_Q$... which I do not know, and don't off-hand know a reference for. | |
| Nov 13, 2018 at 19:56 | comment | added | paul garrett | Indeed... But I figured that it's better to use the less ambiguous term, especially since you already had it in your title. | |
| Nov 13, 2018 at 19:54 | comment | added | Paul Broussous | @paulgarrett Of course you're right! I corrected my mistake. Somehow a parahoric is a parabolic of a certain Tits system ... | |
| Nov 13, 2018 at 19:50 | history | edited | Paul Broussous | CC BY-SA 4.0 |
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| Nov 13, 2018 at 18:57 | comment | added | paul garrett | I gather you mean that $P$ is (most precisely) a parahoric, not parabolic, as in your title? | |
| Nov 13, 2018 at 15:18 | comment | added | Paul Broussous | I realized that there is no tag for "Tits systems" or "BN-pairs". | |
| Nov 13, 2018 at 15:13 | history | asked | Paul Broussous | CC BY-SA 4.0 |