Finite higher spin transformations from exponentiation

Understand

We study the exponentiation of elements of the gauge Lie algebras ${\rm hs}(\lambda)$ of three-dimensional higher spin theories.

• Exponentiable elements generate one-parameter groups of finite higher spin symmetries.
• We show that elements of ${\rm hs}(\lambda)$ in a dense set are exponentiable, when pictured in certain representations of ${\rm hs}(\lambda)$, induced from representations of $SL(2,\mathbb{R})$ in the complementary series.
• We also provide a geometric picture of higher spin gauge transformations clarifying the physical origin of these representations.