Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras

Details Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras

2007-03-06

arxiv.org/abs/math/0703150v1

Mathematics

Representation Theory

Scientific paper

We relate the representations of the rational Cherednik algebras associated with the complex reflection group G(m,1,n) to sheaves on Nakajima quiver varieties associated with extended Dynkin gaphs via a Z-algebra construction. As the parameters defining the Cherednik algebra vary, the stability conditions defining the quiver variety change. We interpret the ordering on category O geometrically using this relationship; we also relate the geometry to the a-function for Hecke algebras with unequal parameters.

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