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SUMMARY:Apoorva Khare (Indian Institute of Science)
DTSTART:20220609T060000Z
DTEND:20220609T070000Z
DTSTAMP:20260423T024518Z
UID:ARCSIN/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ARCSIN/22/">
 Higher order Verma modules\, and a positive formula for all highest weight
  modules - talk 3</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\nIn this final talk\, we continue the study
  of higher order Verma modules and the higher order category $\\mathcal{O}
 ^\\mathcal{H}$ over a Kac–Moody algebra $\\mathfrak{g}$ (one may assume 
 this to be $\\mathfrak{sl}_n$ throughout the talk\, without sacrificing no
 velty). After recalling the definitions\, we explain how BGG reciprocity f
 ails to hold "on the nose"\, yet does hold in a modified form over $\\math
 frak{g} = \\mathfrak{sl}_2^{\\oplus n}$. We then explain BGG resolutions a
 nd Weyl-Kac type character formulas\, for these modules in certain cases. 
 (Joint with G.V.K. Teja.)\n
LOCATION:https://researchseminars.org/talk/ARCSIN/22/
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