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Wednesday, December 7, 2005

**Abstract:** Drinfeld introduced the family of degenerate affine (graded) Hecke algebras attached to any finite group G and its linear finite dimensional complex representation V. I will speak on the ``continuous'' generalization of these algebras, in which the group G is a reductive algebraic group, and V is its algebraic representation. We call this generalization continuous Hecke algebras. They include continuous generalizations of symplectic reflection algebras and rational Cherednik algebras. A motivation for studying continuous Hecke algebras comes from the fact that their representation theory (which is yet to be developed) unifies the representation theories of real reductive groups, Drinfeld-Lusztig degenerate affine Hecke algebras, and symplectic reflection algebras of (in particular, rational Cherednik algebras). This is a joint work with Etingof and Ginzburg.