For a Weyl group W, we give a simple closed formula (valid on elliptic
conjugacy classes) for the character of the representation of W in each
A-isotypic component of the full homology of a Springer fiber. We also give a
formula (valid again on elliptic conjugacy classes) of the W-character of an
irreducible discrete series representation with real central character of a
graded affine Hecke algebra with arbitrary parameters. In both cases, the Pin
double cover of W and the Dirac operator for graded affine Hecke algebras play
key roles.Comment: 15 pages, minor changes in exposition, corrected typo