A new basis for the representation ring of a Weyl group, II

Abstract

In a previous paper I have defined a new basis for the representation ring of a Weyl group. In this paper we show that the new basis is related to the standard basis by an upper triangular unipotent matrix. We also give a new parametrization of representations in a fixed family by certain pairs of subgroups of a finite group attached to the family. We outline an extension to the case of unipotent representations of a finite Chevalley group.

arXiv comment19 pages. This paper is now superseeded by the paper: The Grothendieck group of unipotent representations: a new basis, arxiv:1907.01401