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SUMMARY:Representations of p-adic groups via geometric invariant theory - 
 Beth Romano (University of Cambridge)
DTSTART:20161101T143000Z
DTEND:20161101T153000Z
UID:TALK67455@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Let G be a semisimple split reductive group over a finite exte
 nsion k of Q_p. Reeder\nand Yu have given a new construction of supercuspi
 dal representations of G(k) using geometric\ninvariant theory. Their const
 ruction is uniform for all p but requires as input stable vectors in\ncert
 ain representations coming from Moy–Prasad filtrations. In joint work\, 
 Jessica Fintzen and\nI have classified the representations of this kind wh
 ich contain stable vectors\; as a corollary\, the\nconstruction of Reeder-
 Yu gives new representations when p is small. In my talk\, I will give an\
 noverview of this work\, as well as explicit examples for the case when G 
 = G_2. For these examples\,\nI will explicitly describe the locus of all s
 table vectors\, as well as the Langlands parameters which\ncorrespond unde
 r the local Langlands correspondence to the representations of G(k).
LOCATION:MR13
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