Loop group - Knowlpedia

Definition

Let $G$ be an affine algebraic group over a field $k$ . Its loop group is the group-valued functor

LG(R)=G(R((t)))

on $k$ -algebras $R$ . It records $G$ -valued points on the punctured formal disc.

The positive loop group $L^+G$ is the subfunctor of loops extending across the puncture.

References

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