Central elements in the SLd-skein algebra of a surface

Abstract The SLd SL d -skein algebra Sqₒ₋₃ (S) S SL d q (S) of a surface S is a certain deformation of the coordinate ring of the character variety consisting of flat SLd SL d -local systems over the surface. As a quantum topological object, Sqₒ₋₃ (S) S SL d q (S) is also closely related to the HOMFLYPT polynomial invariant of knots and links in {R}³ R 3. We exhibit a rich family of central elements in Sqₒ₋₃ (S) S SL d q (S) that appear when the quantum parameter q is a root of unity. These central elements are obtained by threading along framed links certain polynomials arising in the elementary theory of symmetric functions, and related to taking powers in the Lie group SLd SL d.