Presenting restricted Steinberg modules of general linear groups

Peter Xu

Presenting restricted Steinberg modules of general linear groups

Representation Theory 2026-07-03 v1 K-Theory and Homology Number Theory

Authors: Peter Xu

Abstract

We give generators and presentations for various local restrictions of Steinberg modules over fields and relate them to \emph{partial} Borel--Serre compactifications of locally symmetric spaces in the case of number fields, extending the existing theory of partial modular symbols for $\mathrm{GL}_2(\Q)$ . Along the way, we clarify the relationship between ``circuit'' and ``Bykovskii''-type presentations for such modules. In an appendix, we relate the existence of such presentations to Koszulity properties of the Steinberg $\mathrm{VB}$ -algebra.

Cite

@article{arxiv.2607.03642,
  title  = {Presenting restricted Steinberg modules of general linear groups},
  author = {Peter Xu},
  journal= {arXiv preprint arXiv:2607.03642},
  year   = {2026}
}