Presentation Name🙍🏼‍♂️🕵️‍♀️: 上海数学中心报告:THE LOCAL LANGLANDS CORRESPONDENCE FOR INNER FORMS OF SL(N)
Presenter: Prof. Roger Plymen
Date: 2014-03-24
Location💇🏼: Room 2201, East Guanghua Tower, Handan Campus
Abstract:

A remarkable feature of the Langlands conjectures is that it is better to consider not just one reductive group at a time, but all inner forms simultaneously. The inner forms of SL_n come about as follows: let F be a nonarchimedean local field and let D be a division algebra, with centre F and dimension d2 over F. With n = md, the kernel of the reduced norm map GL_m(D)→F* is an inner form of SL_n(F). The local Langlands correspondence for inner forms of SL_n(F) is due in characteristic 0 to Hiraga-Saito. In positive characteristic, this result is joint work with Aubert-Baum-Solleveld. I will illustrate this result with the example of SL_2(F) when F is a local function field of characteristic 2. There are countably many supercuspidal L-packets of cardinality 4, and we compute the formal degrees (joint work with Sergio Mendes).

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