On characters of Weyl groups

Weyl Orbit Characters and Schur Functions

For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations. For AN Lie algebras, weight multiplicities can then be calculated by only stating that characters are equivalent to Schur functions. This also means that to calculate characters there is no need to sum over Weyl groups. The compatibility with the Weyl character for...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Parabolic Kazhdan-Lusztig polynomials, plethysm and gereralized Hall-Littlewood functions for classical types

We use power sums plethysm operators to introduce H functions which interpolate between the Weyl characters and the Hall-Littlewood functions Q corresponding to classical Lie groups. The coefficients of these functions on the basis of Weyl characters are parabolic Kazhdan-Lusztig polynomials and thus, are nonnegative. We prove that they can be regarded as quantizations of branching coefficients...

On the Generic Degrees of Cyclotomic Algebras

We determine the generic degrees of cyclotomic Hecke algebras attached to exceptional finite complex reflection groups. The results are used to introduce the notion of spetsial reflection group, which in a certain sense is a generalization of the finite Weyl group. In particular, to spetsial W there is attached a set of unipotent degrees which in the case of a Weyl group is just the set of degr...

Signed Mahonian polynomials for classical Weyl groups

The generating functions of the major index and of the flag-major index, with each of the one-dimensional characters over the symmetric and hyperoctahedral group, respectively, have simple product formulas. In this paper, we give a factorial-type formula for the generating function of the D-major index with sign over the Weyl groups of type D. This completes a picture which is now known for all...

Computational Aspects of Root Systems, Coxeter Groups, and Weyl Characters