p-adic Banach space representations of SL(2, Q_p)

Abstract: We explain how to deduce a classification of admissible unitary representations of SL$(2, \mathbb Q_p)$ on Banach spaces over (finite extensions of) $\mathbb Q_p$ from the $p$-adic Langlands correspondence for GL$(2, \mathbb Q_p)$. The latter was established by Colmez and Colmez-Dospinescu-Paskunas. When the representation is "de Rham'', we relate the corresponding L-packet to the L-packet of associated smooth representations. When compared to the case of smooth representations, interesting similarities as well as dissimilarities can be observed.

number theory

Audience: researchers in the topic

Columbia CUNY NYU number theory seminar