Non-admissible modulo p representations of GL_2(Q_{p^2})

שלחו לחבר
Seminar
Speaker
Prof. Eknath Ghate (Tata Institute of Fundamental Research, Mumbai)
Date
19/08/2020 - 11:30 - 10:30
Place
Zoom invitation below
Abstract

The notion of admissibility of representations of p-adic groups

   goes back to Harish-Chandra. Jacquet and Vigneras have shown that

   smooth irreducible representations of connected reductive p-adic

   groups over algebraically closed fields of characteristic different

   from p are admissible.

 

   The smooth irreducible representations of $\mathrm{GL}_2({\mathbb Q}_p)$

   over $\bar{\mathbb F}_p$ are also known to be admissible, by the

   work of Barthel-Livne, Breuil and Berger.  However, recently Daniel Le

   constructed non-admissible smooth irreducible representations of

   $\mathrm{GL}_2({\mathbb Q}_{p^f})$ over $\bar{\mathbb F}_p$

   for f > 2, where ${\mathbb Q}_{p^f}$ is the unramified extension

   of ${\mathbb Q}_p$ of  degree f. His construction uses a

   diagram (in the sense of Breuil and Paskunas) attached to

   an irreducible mod p representation of the Galois group of

   ${\mathbb Q}_{p^f}$.

 

   We shall speak about a variant of Le's construction in the case f = 2

   which uses instead a diagram attached to a reducible split representation

   of the Galois group of ${\mathbb Q}_{p^2}$. This is joint work

   with Mihir Sheth.

 

=======================================

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Topic: BIU Algebra Seminar -- Ghate

Time: Aug 5, 2020 10:00 AM Jerusalem

 

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