  The subalgebra of diagonal elements of a quantum matrix group has been
conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic
algebra, coined the quantum pseudo-plactic algebra. We present a functorial
approach to the conjecture through the quantum Schur-Weyl duality between the
quantum group and the Hecke algebra. The relations of the quantum diagonal
subalgebra are found to be the image of the braid relations of the underlying
Hecke algebra by an appropriate Schur functor which gives a straightforward
proof of the conjecture.
