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Euler Characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$, and their cohomological consequences
We compute the homological Euler characteristics of $\mathrm{SL}_4(\mathbb{Z})$ and $\mathrm{GL}_4(\mathbb{Z})$ with coefficients in arbitrary irreducible rational highest-weight representations. Applying Wall's formula, we combine the orbifold Euler characteristics of centralizers of torsion elemen
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