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SUMMARY:Michael Harris
DTSTART:20201018T180000Z
DTEND:20201018T183000Z
DTSTAMP:20260418T110219Z
UID:MRTC2020/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MRTC2020/14/
 ">Ramification of supercuspidal parameters</a>\nby Michael Harris as part 
 of The 2020 Paul J. Sally\, Jr. Midwest Representation Theory Conference\n
 \n\nAbstract\nLet $G$ be a reductive group over a local field $F$ of chara
 cteristic $p$.   Genestier and V. Lafforgue have constructed a\nsemi-simpl
 e local Langlands parametrization for irreducible admissible representatio
 ns of $G$\, with values in the $\\ell$-adic points\nof the $L$-group of $G
 $\; the local parametrization is compatible with Lafforgue's global parame
 trization of cuspidal \nautomorphic representations. Using this parametriz
 ation and the theory of Frobenius weights\,  we can define what it \nmeans
  for a representation of $G$ to be "pure". \n\nAssume $G$ is split semisim
 ple.   In work in progress with three collaborators\, whose names will be 
 \nrevealed on October 18\, we have shown that a pure supercuspidal represe
 ntation has ramified local parameter\, \nprovided the field of constants i
 n $F$ has at least $3$ elements and has order prime to the order of the \n
 Weyl group of $G$.  In particular\, if the parameter of a pure representat
 ion $\\pi$ is unramified then $\\pi$ is a\nconstituent of an unramified pr
 incipal series.  We are also able to prove in some cases that the ramifica
 tion is wild.\n
LOCATION:https://researchseminars.org/talk/MRTC2020/14/
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