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The orbit space of the group G := SU(2) × U(1) ⊂ U(3) acting adjointly on the state space of a three-level quantum system is discussed. The semialgebraic structure of is determined within the Procesi–Schwarz method. Using an integrity basis for the ring of G-invariant polynomials , the set of constraints on the Casimir invariants of the group U(3) coming from the positivity requirement...