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SUMMARY:Lucas Mason-Brown (Oxford)
DTSTART:20210208T190000Z
DTEND:20210208T200000Z
DTSTAMP:20260423T004642Z
UID:UMassRep/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMassRep/16/
 ">What is a unipotent representation?</a>\nby Lucas Mason-Brown (Oxford) a
 s part of UMass Amherst Representation theory seminar\n\n\nAbstract\nThe c
 oncept 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 compl
 eted the classification of irreducible representations of G(Fq). He showed
 :\n\n1) All irreducible representations of G(Fq) can be constructed from a
  finite set of building blocks -- called `unipotent representations.'\n\n2
 ) Unipotent representations can be classified by certain geometric paramet
 ers related to nilpotent orbits for a complex group associated to G(Fq).\n
 \nNow\, replace Fq with C\, the field of complex numbers\, and replace G(F
 q) with G(C). There is a striking analogy between the finite-dimensional r
 epresentation theory of G(Fq) and the unitary representation theory of G(C
 ). This analogy suggests that all unitary representations of G(C) can be c
 onstructed from a finite set of building blocks -- called `unipotent repre
 sentations'  -- and that these building blocks are classified by geometric
  parameters related to nilpotent orbits.  In this talk I will propose a de
 finition of unipotent representations\, generalizing the Barbasch-Vogan no
 tion of `special unipotent'. The definition I propose is geometric and cas
 e-free. After giving some examples\, I will state a geometric classificati
 on of unipotent representations\, generalizing the well-known result of Ba
 rbasch-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/UMassRep/16/
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