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By now it is well established that the quantum dimensions of descendants ofthe adjoint representation can be described in a universal form, independent ofa particular family of simple Lie algebras. The Rosso-Jones formula thenimplies a universal description of the adjoint knot polynomials for torusknots, which in particular unifies the HOMFLY (SU_N) and Kauffman (SO_N)polynomials. For E_8 the adjoint representation is also fundamental. We suggestto extend the universality from the dimensions to the Racah matrices and thisimmediately produces a unified description of the adjoint knot polynomials forall arborescent (double-fat) knots, including twist, 2-bridge and pretzel.Technically we develop together the universality and the "eigenvalueconjecture", which expresses the Racah and mixing matrices through theeigenvalues of the quantum R-matrix, and for dealing with the adjointpolynomials one has to extend it to the previously unknown 6x6 case. Theadjoint polynomials do not distinguish between mutants and therefore are notvery efficient in knot theory, however, universal polynomials in higherrepresentations can probably be better in this respect.

Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots