Continuous spin field in the AdS$_6$ space (Part I)

We will discuss the construction of a representation of the $\mathfrak{so}(2,5)$ algebra corresponding to a continuous-spin field in AdS$_6$. Part I. Geometric Formulation of Casimir Operators. In this part of the talk we will describe the realization of the $\mathfrak{so}(2,5)$ algebra using the Lie-Lorentz derivative, which unifies AdS$_6$ geometry and spin degrees of freedom. We will derive explicit expressions for the Casimir operators in terms of the covariant derivative and the spin part of the angular momentum operators.