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SUMMARY:Gurbir Dhillon (Stanford University)
DTSTART:20200527T200000Z
DTEND:20200527T210000Z
DTSTAMP:20260423T040217Z
UID:AG-Davis/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/5/"
 >Steinberg-Whittaker localization and affine Harish--Chandra bimodules</a>
 \nby Gurbir Dhillon (Stanford University) as part of UC Davis algebraic ge
 ometry seminar\n\n\nAbstract\nA fundamental result in representation theor
 y is Beilinson--Bernstein localization\, which identifies the representati
 ons of a reductive Lie algebra with fixed central character with D-modules
  on (partial) flag varieties.  We will discuss a localization theorem whic
 h identifies the same representations instead with (partial) Whittaker D-m
 odules on the group. In this perspective\, representations with a fixed ce
 ntral character are equivalent to the parabolic induction of a 'Steinberg'
  category of D-modules for a Levi.\n\nTime permitting\, we will explain ho
 w these methods can be used to identify a subcategory of Harish--Chandra b
 imodules for an affine Lie algebra and prove that it behaves analogously t
 o Harish--Chandra bimodules with fixed central characters for a reductive 
 Lie algebra. In particular\, it contains candidate principal series repres
 entations for loop groups. This a report on work with Justin Campbell.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/5/
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