Knowlpedia

Definition

Iwahori level structure

A level structure defined by the inverse image of a Borel subgroup under evaluation of positive loops at the marked point.

Definition

Let GG be a over kk, choose a B⊆GB\subseteq G, and let

I={g∈G(k[ ⁣[t] ⁣]):g(0)∈B}.I=\{g\in G(k\lbrack\!\lbrack t\rbrack\!\rbrack):g(0)\in B\}.

An Iwahori level structure on a GG-bundle at a marked point is a to II.

The Iwahori subgroup is a subgroup; equivalently, an Iwahori level structure is a reduction of the fiber at the marked point to BB.

References
  1. Georgios Pappas and Michael Rapoport, “Twisted loop groups and their affine flag varieties,” Advances in Mathematics 219 (2008), 118–198. arXiv.