POLYNOMIAL ALGEBRAS AND HIGHER SPINS

Polynomial relations for the generators of the su(2) Lie algebra in ar bitrary representations are found. They generalize the usual relations for the Pauli operators in the spin 1/2 case and allow one to constru ct modified Holstein-Primakoff transformations in finite-dimensional F ock spaces. The connection between the su(2) Lie algebra and q-oscilla tors with a root of unity q-parameter is considered. The meaning of th e polynomial relations from the point of view of quantum mechanics on a sphere and non-commutative geometry is discussed.