Abstract
We describe all finite-dimensional irreducible linear representations over the field of complex numbers for an arbitrary subgroup of finite index of a Baumslag-Solitar group BS(p, q) = 〈a, t | t−1apt = aq〉 for coprime p and q. We find necessary and sufficient conditions for the equivalence of these representations, using only standard facts of linear algebra and the description of subgroups of finite index in Baumslag-Solitar groups.
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