We introduce the$generic central character$of an irreducible discrete series representation of an affine Hecke algebra. Using this invariant we give a new classification of the irreducible discrete series characters for all abstract affine Hecke algebras (except for the types ${E_{n}^{(1)}}$ , n=6, 7, 8) with$arbitrary positive parameters$and we prove an explicit product formula for their formal degrees (in all cases).

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Let$χ$be an analytic vector field defined in a real-analytic manifold of dimension three. We prove that all the singularities of$χ$can be made elementary by a finite number of blowing-ups in the ambient space.

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