北大数論セミナー：Around irreducibility of parabolic induction for $p$-adic groups(Alberto Mínguez氏)

time：16:30-17:30

Place：理学部3号館3-307

Speaker：Alberto Mínguez 氏（ウィーン大学）

Title：Around irreducibility of parabolic induction for $p$-adic groups

Abstract：
One can use parabolic induction to construct representations of a reductive $p$-adic group $G$. When classifying irreducible representations of $G$, it becomes crucial to identify which parabolically induced representations are irreducible. One of the key tools for studying this problem is the theory of $\rho$-derivatives, and will be introduced during this talk. We will also discuss some open questions, relating representation theory and geometry, and various applications, such as explicating the theta correspondence, the Zelevinsky involution or a new proof of the unitary dual for $GL(n)$ over a non-archimedean field. Some of this work is joint with E. Lapid, H. Atobe and T. Lanard.

Organizer：跡部 発、安田 正大