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SUMMARY:Monica Vazirani (UC Davis)
DTSTART:20210329T180000Z
DTEND:20210329T190000Z
DTSTAMP:20260423T004545Z
UID:UMassRep/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UMassRep/28/
 ">Elliptic Schur-Weyl duality and representations of the DAHA</a>\nby Moni
 ca Vazirani (UC Davis) as part of UMass Amherst Representation theory semi
 nar\n\n\nAbstract\nBuilding on the work of Calaque-Enriquez-Etingof\, Lyub
 ashenko-Majid\,\nand Arakawa-Suzuki\, Jordan constructed a functor from qu
 antum D-modules\non special linear groups to representations of the double
  affine Hecke\nalgebra (DAHA) in type A.  When we input quantum functions 
 on GL(N) the\noutput is L(k^N)\, the irreducible DAHA representation index
 ed by an N\nby k rectangle.  For the specified parameters\, L(k^N) is Y-se
 misimple\,\ni.e. one can diagonalize the Dunkl operators.  We give an expl
 icit\ncombinatorial description of this module via its Y-weight basis in\n
 terms of skew tableaux\, or equivalently\,  periodic tableaux of\nrectangu
 lar shape. \nThis is joint work with David Jordan.\nIf time allows\, I wil
 l talk about work  in progress with \nSam Gunningham and David Jordan on t
 he \nquantum Hotta-Kashiwara D-modules\, their endomorphim algebras\,\nand
  which DAHA representations they become after applying Jordan's\nelliptic 
 Schur-Weyl functor.\n
LOCATION:https://researchseminars.org/talk/UMassRep/28/
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