Characters and chromatic symmetric functions

Given a poset P, let inc(P) be its incomparability graph, and X-inc(P) the corresponding chromatic symmetric function defined by Stanley in Adv. Math., 111 (1995) pp. 166{194. Let omega be the standard involution on symmetric functions. We express coefficients of X-inc(P) and omega X-inc(P) as character evaluations to obtain simple combinatorial interpretations for coefficients of the power sum and monomial expansions of omega X-inc(P) which hold for all posets P. Consequences include new combinatorial interpretations of the permanent, induced trivial character immanants, and power sum immanants of totally nonnegative matrices, and of the sum of elementary coefficients in the Shareshian-Wachs chromatic quasisymmetric function X-inc(P);q when P is an appropriately labeled unit interval order.