
Journal of Lie Theory 21 (2011), No. 4, 771785 Copyright 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 1764, Bucharest, Romania Ingrid.Beltita@imar.ro Daniel Beltita Institute of Mathematics "Simion Stoilow", Romanian Academy of Sciences, P. O. Box 1764, Bucharest, Romania Daniel.Beltita@imar.ro [Abstractpdf] \def\g{{\frak g}} We address a linearity problem for differentiable vectors in representations of infinitedimensional 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 [ Fulltextpdf (280 KB)] for subscribers only. 