Positive loop group - Knowlpedia

Definition

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

L^+G(R)=G(R\lbrack\!\lbrack t\rbrack\!\rbrack)

on $k$ -algebras $R$ . The inclusion $R\lbrack\!\lbrack t\rbrack\!\rbrack\subset R((t))$ identifies $L^+G$ as a subgroup of the loop group $LG$ .

References

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