Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials

We obtain the Kirillov vector fields on the set of functions $f$ univalent inside the unit disk, in terms of the Faber polynomials of $1\mathrm{/}f(1\mathrm{/}z)$. Our construction relies on the generating function for Faber polynomials.