User:JayBeeEll/Affine symmetric group
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Now published at WJS, and incorporated into Wikipedia as Affine symmetric group.
Some things that I don't already have sources for but might be worth adding:
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- from the combinatorial perspective, it's ``affine permutations whose last window entry is n (right??)
- from the geometric, we can find as those vectors with last coordinate 0, and it's the transformations that stabilize this sublattice (right??)
- from the algebraic, we send for and (right??)
- these maps make it a sub-reflection group, but not a parabolic subgroup (in any sense of the word)
- from the combinatorial perspective, for any integer k, but this inclusion is not as reflection groups. Is there a geometric explanation for this action? Is it of any use to anyone else for any reason?
- as a consequence of the previous, we can see that the set of all affine permutations is a group. I know this has appeared in a (unpublished?) paper of Abrams--Cowen-Morton; has it ever appeared anywhere else?