The ring of stable characters over GL.(q)

Fix a prime power . The ring of stable characters over the family of groups  is a natural and useful ring of class functions defined simultaneously on (almost) every group in the family and has nice features. We show that four different sets of functions, each defined in a different setting, are all linear bases for this ring, leading to some interesting corollaries. This ring and these four classes of functions have better-known analogs for symmetric groups, which I will mention.

This is joint work with Doron Puder and Yotam Shomroni.