Principal series representations and p-adic Langlands program

Type: 
PhD Student Seminar
Audience: 
Open to the Public
Building: 
Zrinyi u. 14
Room: 
310/A
Wednesday, March 26, 2014 - 2:00pm
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Date: 
Wednesday, March 26, 2014 - 2:00pm to 3:30pm

Abstract: The Langlands philosophy predicts a "nice" bijection between certain type of irreducible representations of the group GL_n(Q_p) over the p-adic field Q_l, and certain n-dimensional Galois representations. If l and p are different the correspondence is quite well understood, but it is not clear what shall be done if l=p. Some developments were done in the past years: Colmez completely solved the case n=2, and parts of his work were generalized by Schneider and Vigneras.
The simplest irreducible representations of the group GL_n(Q_p) are the irreducible ones among the so called principal series representations. I will talk about these representations, and their image under the Schneider-Vigneras D-functor.