University of Birmingham > Talks@bham > Algebra Seminar > Dirac operators and Hecke algebras

Dirac operators and Hecke algebras

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If you have a question about this talk, please contact Chris Parker.

I will explain the construction and main properties of Dirac operators for representations of various Hecke-type algebras (e.g., Lusztig’s graded Hecke algebra for p-adic groups, Drinfeld’s Hecke algebras, rational Cherednik algebras). The approach is motivated by the classical Dirac operator which acts on sections of spinor bundles over Riemannian symmetric spaces, and by its algebraic version for Harish-Chandra modules of real reductive groups. The algebraic Dirac theory developed for these Hecke algebras turns out to lead to interesting applications: e.g., a Springer parameterization of projective representations of finite Weyl groups (in terms of the geometry of the nilpotent cone of complex semisimple Lie algebras), spectral gaps for unitary representations of reductive p-adic groups, connections between the Calogero-Moser space and Kazhdan-Lusztig double cells. I will present some of these applications in the talk.

This talk is part of the Algebra Seminar series.

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