Introduction to Local Langlands Correspondence
>
Mahdi Asgari
(Oklahoma State University)
 .
Abstract As part of his overall program, R. P. Langlands conjectured a certain correspondence between the set of (equivalence classes of) irreducible smooth representations of a $p$-adic reductive group and its set of $L$-parameters, i.e., certain admissible homomorphisms from the Weil group of the $p$-adic field to a certain complex group, called the $L$-group. This parameterization is to satisfy various number theoretic and representation theoretic properties involving $L$-functions and $\epsilon$-factors among other things, and lies, along with its global conjectural analogue, at the heart of the modern theory of automorphic forms and representations.  When the group is $GL_n$ the correspondence is actually a bijection, now a theorem due to Michael Harris & Richard Taylor as well as Guy Henniart (around 2001) and Peter Scholze again more recently (around 2013).
>
I will review some of these subjects and try to report on a recent work, joint with Kwangho Choiy, establishing the Local Langlands Conjecture for small rank general spin groups and their inner forms.
.
Date: Wed Jan 6
.
Time: 15:30-17
 .
Location: Lecture Hall 2, Niavaran Building, IPM

پاسخ دهید

نشانی ایمیل شما منتشر نخواهد شد. بخش‌های موردنیاز علامت‌گذاری شده‌اند *