A Quantum Deformation of Invariants of Higher Binary Forms

We use the theory of the quantum group Uq(gl(2, )) to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan–Capelli series. Higher binary forms are introduced on the basis of braided algebras. We define quantised invariants and give basic examples. We show that the symbolic method of Clebsch and Gordan works also in the quantised case. We discuss the deformed discriminant of the quadratic and the cubic form, the deformed invariants I1, I2 of the quartic form and further invariants without a classical analog.