Invariant derivations and trace bounds
Representation Theory
2025-09-04 v4 Group Theory
Abstract
About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note provides a new, general method for proving such bounds; uses that method to derive Serre's bounds; gives a second proof of Serre's announced results that (we learned) closely follows his original argument; and provides lower bounds for traces of other representations of compact Lie groups and for Brauer characters of finite groups.
Keywords
Cite
@article{arxiv.2312.03101,
title = {Invariant derivations and trace bounds},
author = {Skip Garibaldi and Robert M. Guralnick and Eric M. Rains},
journal= {arXiv preprint arXiv:2312.03101},
year = {2025}
}
Comments
v4 has small improvements to the exposition. v3 re-writes part I, expands other parts of the text, and adds an appendix on finite groups. v2 strengthens the results of part IV