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.