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

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

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.



Michael Schein is inviting you to a scheduled Zoom meeting.


Topic: BIU Algebra Seminar -- Ghate

Time: Aug 5, 2020 10:00 AM Jerusalem


Join Zoom Meeting


Meeting ID: 318 532 3623

Passcode: 142857