# Dan M. Barbasch

## Professor

## Research Focus

Representation theory of reductive Lie groups

My research is in the field of representation theory of reductive Lie groups. I am particularly interested in the classification of the unitary dual for groups over local fields, and its relation to the orbit structure of the Lie algebra. Furthermore I am interested in the relation of these representations to problems arising from number theory, more precisely automorphic forms.

## Publications

- Dirac index and twisted characters (with P. Pandzic and P. Trapa), arxiv.org/pdf/1606.05425.pdf, preprint.
- Dirac cohomology for graded affine Hecke algebras (with D.Ciubotaru and P. Trapa), Acta Math. 209 (2012), no. 2, 197-227.
- Spherical unitary dual for split real and p-adic groups, J. of the Mathematical Institute Jussieu, vol 9 (2010), issue 02, 265-356.
- Reduction to real infinitesimal character in affine Hecke algebras (with A. Moy), Journal of the AMS 6 no. 3 (1993), 611-635.
- The Langlands classification and irreducible characters (with J. Adams and D. Vogan), Birkhauser (1992), Boston-Basel-Berlin.
- Unipotent representations for real reductive groups, Proceedings of ICM, Kyoto 1990 (1990), Springer-Verlag, Math. Soc. of Japan, 769-777.
- The unitary dual of complex classical groups, Inv. Math. 96 (1989), 103-176.
- Unipotent representations of complex classical groups (with D. Vogan), Ann. Math. 121 (1985), 41-110.