Power sum elements in the G2 skeinalgebra

We study the skein algebras of surfaces associated to the exceptional Lie group G 2 , using Kuperberg webs.We identify two 2-variable polynomials, P n .x;y/ and Q n .x;y/, and use threading operations along knots to construct a family of central elements in the G 2 skein algebra of a surface, S G 2 q ./, when the quantum parameter q is a 2n th root of unity.We verify these elements are central using elementary skein-theoretic arguments.We also obtain a result about the uniqueness of the so-called transparent polynomials P n and Q n .Our methods involve a detailed study of the skein modules of the annulus and the twice-marked annulus.