The Category O for a General Coxeter System

Complete Growth Series of Coxeter Groups with more than Three Generators

Kazhdan-Lusztig-Stanley polynomials and quadratic algebras I M.J.Dyer

In [KL], Kazhdan and Lusztig associate a polynomial to each Bruhat interval in a Coxeter group; some of these “Kazhdan-Lusztig” polynomials now play an important role in several areas of representation theory. A similar family of polynomials has been associated to face latices of convex polytopes (see Stanley [St]). Both families of polynomials remain poorly understood in general, though they a...

DIAGONAL COINVARIANTS OF Zm ≀ Sn

We construct a quotient ring of the ring of diagonal coinvariants of the complex reflection group W = G(m, 1, n) and determine its graded character. This generalises a result of Gordon for Coxeter groups. The proof uses a study of category O for the rational Cherednik algebra of W , including a shift isomorphism which is proved in Appendix 1.

in Algebra . Coxeter groups and Hecke algebras

The finite Coxeter groups are the finite groups generated by reflections on real Euclidean spaces. Examples include dihedral groups, the symmetry groups of regular polytopes (e.g. regular polygons and platonic solids) and the Weyl groups of semisimple complex Lie groups and Lie algebras (such as the special linear group and Lie algebra). General Coxeter groups may be defined as certain (special...

POLYNOMIALS ATTACHED TO REPRESENTATIONS OF G ( r , p , n )

The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group. There is a category O of modules for this algebra which is a highest weight category. For the infinite family G(r, p, n) of complex reflection groups, the algebra H contains a subalgebra isomorphic to a (generalized) degenerate affine Hecke algebra, and our strategy...