Maria Chlouveraki
Published 2013-11-28, updated 2014-01-20Version 2
The current article is a short survey on the theory of Hecke algebras, and in particular Kazhdan-Lusztig theory, and on the theory of symplectic reflection algebras, and in particular rational Cherednik algebras. The emphasis is on the connections between Hecke algebras and rational Cherednik algebras that could allow us to obtain a generalised Kazhdan-Lusztig theory, or at least its applications, for all complex reflection groups.
Comments: This survey was written for the Proceedings of the MSRI Introductory Workshop in Noncommutative Algebraic Geometry and Representation Theory (2013)
Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras
Geodesic Normal Forms and Hecke Algebras for the Complex Reflection Groups G(de,e,n)
Dirac cohomology for symplectic reflection algebras
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