Introduction to Local Langlands Correspondence
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Mahdi Asgari
(Oklahoma State University)
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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).
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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.
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Date: Wed Jan 6
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Time: 15:30-17
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Location: Lecture Hall 2, Niavaran Building, IPM