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Characters of Springer representations on elliptic conjugacy classes. (English) Zbl 1260.22012

For a Weyl group \(W,\) the authors investigate simple closed formulas (valid on elliptic conjugacy classes) for the character of the representation of \(W\) in the homology of a Springer fiber. They 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.

MSC:

22E50 Representations of Lie and linear algebraic groups over local fields
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References:

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