2 added 580 characters in body

Let's say

Let me take this question again from the top.

I have would like to know what a friend (it's plausible, right?)special parahoric subgroup is.This friend has

I think this is a PhD in mathematics and some experience in arithmetic geometry"real" question, including some familiarity with Shimura varieties. In factthough not an especially good one -- it indicates my complete lack of expertise in this area, his overall background but it is remarkably similar certainly a question of interest to my ownresearch mathematicians (who else?). However, for some

The reason this friend -- who, once again, is essentially as learned as that I am want to know -- has no idea what and that I would prefer a special parahoric subgroupshort, relatively simple answer rather than an invitation to read the original paper of Bruhat and Tits -- is that I have been asked to write a reductive $p$-adic group might be. He's even MathReview for a little bit embarrassed about itpaper using this concept.

Rather than helping him directlyNow, perhaps I shouldn't have decided agreed to draw on review this paper, and I didn't, exactly, but it was sent to me about three months ago so it seems a little late to object. Anyway, the collective expertise introduction is clear, so I think my final product will be a reasonable specimen of this site: what would you tell the form. It's just that, for my friend?

P.S.: He own benefit, when I write sentences like

"The stabilizer of a self-dual periodic lattice chain is expecting an answer a parahoric subgroup (or, in terms some cases, contains a parahoric subgroup of index 2, which one recovers by intersecting with the associated Bruhat-Tits buildingkernel of the Kottwitz homomorphism). He's not completely comfortable with that, but understands that that's what he's probably going The author restricts to getsubsets $I$ for which the parahoric so obtained is special in the sense of Bruhat-Tits theory."

it would be nice if I understood a little better what that meant.

He also says

I am looking ideally for a quick answer that giving increases my knowledge at least a reference would probably be acceptable, but please not to refer him little bit together with a place to read up on it when I get the original paper of Bruhat and Titstime / inclination to deepen my knowledge.

Post Made Community Wiki by Pete L. Clark
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# What is a special parahoric subgroup?

Let's say I have a friend (it's plausible, right?). This friend has a PhD in mathematics and some experience in arithmetic geometry, including some familiarity with Shimura varieties. In fact, his overall background is remarkably similar to my own. However, for some reason this friend -- who, once again, is essentially as learned as I am -- has no idea what a special parahoric subgroup of a reductive $p$-adic group might be. He's even a little bit embarrassed about it.

Rather than helping him directly, I have decided to draw on the collective expertise of this site: what would you tell my friend?

P.S.: He is expecting an answer in terms of the associated Bruhat-Tits building. He's not completely comfortable with that, but understands that that's what he's probably going to get.

He also says that giving a reference would probably be acceptable, but please not to refer him to the original paper of Bruhat and Tits.