BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Lucas Mason-Brown (University of Oxford)
DTSTART:20210428T203000Z
DTEND:20210428T213000Z
DTSTAMP:20260423T035411Z
UID:MITLie/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/29/">
 What is a unipotent representation?</a>\nby Lucas Mason-Brown (University 
 of Oxford) as part of MIT Lie groups seminar\n\nLecture held in 2-142.\n\n
 Abstract\nThe concept of a unipotent representation has its origins in the
  representation theory of finite Chevalley groups. Let G(Fq) be the group 
 of Fq-rational points of a connected reductive algebraic group G. In 1984\
 , Lusztig completed the classification of irreducible representations of G
 (Fq). He showed:\n\n1) All irreducible representations of G(Fq) can be con
 structed from a finite set of building blocks -- called `unipotent represe
 ntations.'\n\n2) Unipotent representations can be classified by certain ge
 ometric parameters related to nilpotent orbits for a complex group associa
 ted to G(Fq).\n\nNow\, replace Fq with C\, the field of complex numbers\, 
 and replace G(Fq) with G(C). There is a striking analogy between the finit
 e-dimensional representation theory of G(Fq) and the unitary representatio
 n theory of G(C). This analogy suggests that all unitary representations o
 f G(C) can be constructed from a finite set of building blocks -- called `
 unipotent representations' -- and that these building blocks are classifie
 d by geometric parameters related to nilpotent orbits. In this talk I will
  propose a definition of unipotent representations\, generalizing the Barb
 asch-Vogan notion of `special unipotent'. The definition I propose is geom
 etric and case-free. After giving some examples\, I will state a geometric
  classification of unipotent representations\, generalizing the well-known
  result of Barbasch-Vogan for special unipotents.\n\nThis talk is based on
  forthcoming joint work with Ivan Loseu and Dmitryo Matvieievskyi.\n
LOCATION:https://researchseminars.org/talk/MITLie/29/
END:VEVENT
END:VCALENDAR