Thu, 23 Apr 2026
11:00
11:00
L4
Upper bound to the GK-dimension for p-adic Banach representations with infinitesimal character
Reinier Sorgdrager
(University of Amsterdam and Université Paris-Saclay)
Abstract
Let p>2 and K be a finite extension of Q_p. In recent work I have shown that an admissible p-adic Banach representation of GL2(K) has Gelfand-Kirillov dimension at most the degree [K:Q_p] as soon as its locally analytic vectors have an infinitesimal character. In work yet to appear I adapt its method to 'p-adic Banach representations in families with infinitesimal characters in families' -- still for GL2(K).
I will briefly motivate the result by some consequences to the p-adic Langlands program, such as a generalization of the GK-bound of Breuil-Herzig-Hu-Morra-Schraen beyond K unramified. Then I will give a quick overview of the above notions and try to present the key idea of the proof, for a single representation and with K=Q_p.