# rt.representation theory – Computing explicit matrix coefficients

I would like to understand in a more explicit way the Fell topology on unitary duals, that is to say the convergence of matrix coefficients of local representations.

If I consider a local representation $$pi_lambda$$ of a certain type (e.g. principal series for $$GL(2)$$ over a non-archimedean field), I would like to get an explicit dependence of the matrix coefficient $$langle pi_lambda(g)v, wrangle_lambda$$ in terms of the parameter $$lambda$$. This in particular involve explicit choices of a model for the representation and specific vectors: has this been done explicitly somewhere?

Ultimately, I want to see to what extent the Fell topology on representations corresponds to the usual topology on its (finite-dimensional) parameters.