Characters of Springer representations on elliptic conjugacy classes

Details Characters of Springer representations on elliptic conjugacy classes Characters of Springer representations on elliptic conjugacy classes

2011-05-20

arxiv.org/abs/1105.4113v2

Mathematics

Representation Theory

15 pages, minor changes in exposition, corrected typos

Scientific paper

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.

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