Description
The Gelfand-Kirillov dimension is an invariant of p-adic representations of p-adic Lie groups. It is a generalization of the Krull dimension to (non-commutative) completed group rings. Precise knowledge of this dimension can lead to interesting applications to the p-adic Langlands program and completed cohomology, as observed by Gee--Newton.
In my talk I will introduce the above dimension and then discuss the following result from my thesis: let K be a p-adic field, then any admissible p-adic Banach representation of GL_2K admitting an infinitesimal character has Gelfand-Kirillov dimension at most [K:Q_p]. I have also proved a version in families of the above result.
I will briefly mention some applications and I hope to sketch the proof in the case of K=Q_p.