On differentiability of vectors in Lie group representations

TL;DR

This paper investigates the conditions under which vectors in infinite-dimensional Lie group representations exhibit differentiability properties, focusing on the linearity of their directional derivatives in locally convex spaces.

Contribution

It introduces a new approach to analyze the differentiability of vectors in infinite-dimensional Lie group representations, extending classical results to more general settings.

Findings

Established criteria for differentiability of vectors in Lie group representations.

Extended linearity results to infinite-dimensional contexts.

Provided insights into the structure of differentiable vectors in locally convex spaces.

Abstract

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.