A QUANTUM DEFORMATION OF INVARIANTS OF BINARY FORMS*)

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Abstract

The modern representation theory has its roots in the classical theory of invariants of binary forms of Caley, Silvester, Clebsch, Gordan, Capelli etc. We use the theory of the quantum group Uq(sl(2, Symbol 1) in order to develop a quantum theory of invariants. 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 calculate the quantised discriminant of the quadratic form, the quantised catalecticant of the quartic form and further invariants without a classical analogon.

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