## Duke Mathematical Journal

### Characters of Springer representations on elliptic conjugacy classes

#### Abstract

For a Weyl group $W$, we investigate simple closed formulas (valid on elliptic conjugacy classes) for the character of the representation of $W$ in the 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.

#### Article information

Source
Duke Math. J., Volume 162, Number 2 (2013), 201-223.

Dates
First available in Project Euclid: 24 January 2013

https://projecteuclid.org/euclid.dmj/1359036934

Digital Object Identifier
doi:10.1215/00127094-1961735

Mathematical Reviews number (MathSciNet)
MR3018954

Zentralblatt MATH identifier
1260.22012

#### Citation

Ciubotaru, Dan M.; Trapa, Peter E. Characters of Springer representations on elliptic conjugacy classes. Duke Math. J. 162 (2013), no. 2, 201--223. doi:10.1215/00127094-1961735. https://projecteuclid.org/euclid.dmj/1359036934

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