Characters of Springer representations on elliptic conjugacy classes

Dan M. Ciubotaru, Peter E. Trapa
2013 Duke mathematical journal  
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.
doi:10.1215/00127094-1961735 fatcat:f6bjutnvarc6tleljbmkrcokiq