Epsilon systems on geometric crystals of type .
Erratum to the paper "Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle".
Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects
We show that for any strongly closed subgroup of a unitary group of a finite von Neumann algebra, there exists a canonical Lie algebra which is complete with respect to the strong resolvent topology. Our analysis is based on the comparison between measure topology induced by the tracial state and the strong resolvent topology we define on the particular space of closed operators on the Hilbert space. This is an expository article of the paper by both authors in Hokkaido Math. J. 41 (2012), 31-99,...
Explicit description of a family of affine Kac-Moody groups. (Description explicite d'une famille de groupes de Kac-Moody affines.)