Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 21 (2011), No. 4, 771--785Copyright Heldermann Verlag 2011 On Differentiability of Vectors in Lie Group Representations Ingrid Beltita Institute of Mathematics "Simion Stoilow", Romanian Academy of Sciences, P. O. Box 1-764, Bucharest, Romania Ingrid.Beltita@imar.ro Daniel Beltita Institute of Mathematics "Simion Stoilow", Romanian Academy of Sciences, P. O. Box 1-764, Bucharest, Romania Daniel.Beltita@imar.ro [Abstract-pdf] \def\g{{\frak g}} We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions. In particular, we find conditions ensuring that if $\pi\colon G\to{\rm End}({\cal Y})$ is such a representation, and $y\in{\cal Y}$ is a vector such that ${\rm d}\pi(x)y$ makes sense for every $x$ in the Lie algebra $\g$ of $G$, then the mapping ${\rm d}\pi(\cdot)y\colon\g\to{\cal Y}$ is linear and continuous. Keywords: Lie group, topological group, unitary representation, smooth vector. MSC: 22E65; 22E66, 22A10, 22A25 [ Fulltext-pdf  (280  KB)] for subscribers only.