| Résume | I will discuss two results on the growth of dimensions of fixed vectors of representations π of p-adic GLN under principal congruence subgroups: First, a uniform bound on the growth of fixed vectors in terms of the GK-dimension of π. Second, for π unitary, a quantitative relationship between the GK-dimension of π and the rate of decay of its matrix coefficients. These results are motivated by global applications, namely approximations to the Ramanujan conjecture. They are independent of one another and proved in the framework of the Langlands and Zelevinsky classification. This is joint work with Rahul Dalal and Simon Marshall. |
