Equivariant Euler characteristics of the symplectic building

TL;DR

This paper calculates the equivariant Euler characteristics for the action of a finite symplectic group on its associated building, providing insights into the topological and algebraic structure of these mathematical objects.

Contribution

It introduces a method to compute equivariant Euler characteristics for symplectic groups acting on their buildings, a novel approach in this area.

Findings

Explicit formulas for equivariant Euler characteristics

Enhanced understanding of symplectic group actions

New techniques for topological invariants in algebraic groups

Abstract

We determine the equivariant Euler characteristics for the action of a finite symplectic group on its building.