Cohomologie T-équivariante de la variété de drapeaux d'un groupe de Kač-Moody
Construction d'un groupe de Kac-Moody et applications
Contractibilité du groupe linéaire des espaces de Hilbert de dimension infinie
Déformations des structures complexes sur les espaces homogènes de SL (2, ...).
Demazure character formula in arbitrary Kac-Moody setting.
Description of infinite-dimensional abelian regular Lie groups.
Direct limits of Zuckerman derived functor modules.
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.)
Factor representations of diffeomorphism groups
We give a new construction of semifinite factor representations of the diffeomorphism group of euclidean space. These representations are in canonical correspondence with the finite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a generalization of complete positivity as developed in operator algebras....
Faithful Representations and a Local Property of Lie Groups.
Finite dimensional modules of some quantum groups over Fp (v).
Finite-dimensional Lie subalgebras of algebras with continuous inversion
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute...
Geometry of Poisson structures.
Groupes associés aux algèbres de Kac-Moody
Groups of -diffeomorphisms related to a foliation
The notion of a -diffeomorphism related to a foliation is introduced. A perfectness theorem for the group of -diffeomorphisms is proved. A remark on -diffeomorphisms is given.
Groups of diffeomorphisms and Lie theory.
Groups of strings.