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# Johannes Flake – Geometric Methods in Representation Theory Seminar

## February 9, 2018 @ 4:00 pm - 5:00 pm

**Title: **

*Dirac cohomology, Hopf-Hecke algebras, and infinitesimal Cherednik algebras*

**Abstract:**Dirac operators have played an important role in the representation theory of reductive Lie groups, but also of various Hecke algebras. We show how these cases can be studied uniformly, using smash products of Hopf algebras, PBW deformations, and superalgebras. We prove a generalized version of a result known as Vogan’s conjecture in certain special cases, which relates Dirac cohomology with central characters. We discuss infinitesimal Cherednik algebras as a novel special case, and we obtain partial results on the classification of the class of algebras to which our theory applies.