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SUMMARY:David Vogan (MIT)
DTSTART:20220804T143000Z
DTEND:20220804T160000Z
DTSTAMP:20260422T150459Z
UID:atlas/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/atlas/31/">D
 uality for singular and non-integral infinitesimal character</a>\nby David
  Vogan (MIT) as part of Real reductive groups/atlas\n\n\nAbstract\nJeffrey
  Adams explained in the last two lectures how Vogan duality relates repres
 entation of a real group G(R) to representations of a real form G^v(R) of 
 the Langlands dual group\, in the case of regular integral infinitesimal c
 haracter. Today I have three goals:\n     1) to say a few words about how 
 this representation theory duality can be rephrased as\n\n(reps of G(R))  
 DUAL TO  (algebraic geometry of space of Langlands parameters in ^L G)\n\n
 so that it can make sense over other local fields\;\n\n     2) Explain wha
 t happens for regular but NON integral infinitesimal character. (Answer: r
 eal form of G^v is replaced by real form of pseudolevi subgroup G^v(gamma)
 ).\n\n     3) Explain what happens for SINGULAR infinitesimal character. (
 Answer: translation principle  tells you everything\, but what it tells yo
 u is a bit complicated.)\n\nThe subgroup G^(gamma) is dual to a Langlands-
 Shelstad endoscopic group for G. What we do with G^(gamma) is certainly re
 lated to endoscopy\, but it is not at all precisely the same thing.\n
LOCATION:https://researchseminars.org/talk/atlas/31/
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