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

`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 - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`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

Last Updated Date : 29/07/2020