Apartment classes of integral symplectic groups

Abstract

In this note we present an alternative proof of a theorem of Gunnells, which states that the Steinberg module of $\mathrm{S}{\mathrm{p}}_{2n}(\mathbb{Q})$ is a cyclic $\mathrm{S}{\mathrm{p}}_{2n}(\mathbb{Z})$-module, generated by integral apartment classes.

v2: 16 pages. References updated. v3: accepted version, to appear in J. Topol. Anal