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

Seminar
Speaker
Prof. Eknath Ghate (Tata Institute of Fundamental Research, Mumbai)
Date
19/08/2020 - 11:30 - 10:30Add to Calendar 2020-08-19 10:30:00 2020-08-19 11:30:00 Non-admissible modulo p representations of GL_2(Q_{p^2}) 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 https://zoom.us/j/3185323623?pwd=NzJncWZVV1dJQXZSSDlralk1d3NsZz09   Meeting ID: 318 532 3623 Passcode: 142857 Zoom invitation below אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Zoom invitation below
Abstract

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

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

https://zoom.us/j/3185323623?pwd=NzJncWZVV1dJQXZSSDlralk1d3NsZz09

Meeting ID: 318 532 3623

Passcode: 142857

תאריך עדכון אחרון : 29/07/2020