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SUMMARY:Apoorva Khare (Indian Institute of Science)
DTSTART:20220520T060000Z
DTEND:20220520T070000Z
DTSTAMP:20260423T004700Z
UID:ARCSIN/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/20/">
 Higher order Verma modules\, and a positive formula for all highest weight
  modules - talk 1</a>\nby Apoorva Khare (Indian Institute of Science) as p
 art of ARCSIN - Algebra\, Representations\, Combinatorics and Symmetric fu
 nctions in INdia\n\n\nAbstract\nWe study weights of highest weight modules
  $V$ over a Kac-Moody algebra $\\mathfrak{g}$ (one may assume this to be $
 \\mathfrak{sl}_n$ throughout the talk\, without sacrificing novelty). We b
 egin with several positive weight-formulas for arbitrary non-integrable si
 mple modules\, and mention the equivalence of several "first order" data t
 hat helps prove these formulas. We then discuss the notion of "higher orde
 r holes" in the weights\, and use these to present two positive weight-for
 mulas for arbitrary modules $V$. One of these is in terms of "higher order
  Verma modules". (Joint with G.V.K. Teja and with Gurbir Dhillon.)\n
LOCATION:https://researchseminars.org/talk/ARCSIN/20/
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