Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras
Representation Theory
2007-05-23 v1 Algebraic Geometry
Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.math/0703150,
title = {Quiver varieties, category O for rational Cherednik algebras, and Hecke algebras},
author = {Iain Gordon},
journal= {arXiv preprint arXiv:math/0703150},
year = {2007}
}