Linear limits of irreducible characters

TL;DR

This paper establishes new theoretical bounds on the limits of irreducible characters in group theory, simplifying previous complex proofs and providing a clearer understanding of stabilizer limits.

Contribution

It introduces a streamlined proof of a main theorem related to stabilizer limits of irreducible characters, improving upon earlier complicated arguments.

Findings

Proves a main theorem on stabilizer limits of irreducible characters.

Simplifies previous proofs with more elegant arguments.

Provides foundational results applicable to character theory in finite groups.

Abstract

Nearly twenty years ago Isaacs and the first author of this paper wrote a series of articles \cite{isa2}, \cite{da3}, \cite{da2} about what were called ``stabilizer limits'' of group characters, following the terminology of Berger \cite{be}. The second author, in her thesis \cite{lo}, needed one of the results of those articles in a new situation which was not treated earlier. Eventually she was able, by complicated and delicate arguments, to reduce her proof to a special case where \cite[Theorem 8.4]{da3} could be applied. But this approach was extremely awkward. In the present paper we use arguments similar to those in the earlier articles to prove a Main Theorem from which the exact Theorem A needed in \cite{lo} easily follows.