Arithmetic Representation Growth of Virtually Free Groups

2022/01/28 by Fabian Korthauer, Korthauer, Fabian
Mathematics · #14D20 #14L30 #16G99 #20C07 #32S35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2201.12319

openalex publication_date 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 GL_d(ℂ)-character varieties of virtually free groups. As examples we discuss the representation theory of \mathbbD_∞ , PSL₂(ℤ) , SL₂(ℤ) , GL₂(ℤ) and PGL₂(ℤ) .

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