On the local coefficients matrix for coverings of SL₂

We discuss the Gelfand–Kazhdan criterion for covering groups with abelian covering tori and also investigate several aspects of the local coefficients matrix for genuine principal series representations of coverings of SL₂. The goal is to carry out some preliminary study on some invariants attached to the local coefficients matrix, with a view toward a theory of γ -factors and L-functions for genuine representations of covering groups.