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arXiv · 2201.12319

Arithmetic Representation Growth of Virtually Free Groups

Fabian Korthauer
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Abstract

We adapt methods from quiver representation theory and Hall algebra techniques to the counting of representations of virtually free groups over finite fields. This gives rise to the computation of the E-polynomials of $\mathbf{GL}_d(\mathbb{C})$-character varieties of virtually free groups. As examples we discuss the representation theory of $\mathbb{D}_\infty$ , $\mathbf{PSL}_2(\mathbb{Z})$ , $\mathbf{SL}_2(\mathbb{Z})$ , $\mathbf{GL}_2(\mathbb{Z})$ and $\mathbf{PGL}_2(\mathbb{Z})$ .

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BibTeXRIS

Fabian Korthauer. 2022-01-28. Arithmetic Representation Growth of Virtually Free Groups. https://arxiv.org/abs/2201.12319

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