Bulk irreducibles of the modular group

As the 3-string braid group B3 and the modular group Γ are both of wild representation type one cannot expect a full classification of all their finite dimensional simple representations. Still, one can aim to describe 'most' irreducible representations by constructing for each d-dimensional irreducible component X of the variety issn(Γ) classifying the isomorphism classes of semi-simple n-dimensional representations of Γ an explicit minimal étale rational map &#x1d538;d → X having a Zariski dense image. Such rational dense parametrizations were obtained for all components when n < 12 in [5]. The aim of the present paper is to establish such parametrizations for all finite dimensions n.

Publication year:2016