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SUMMARY:Hitoshi Konno: Elliptic Quantum Toroidal Algebra $U_{q\,t\,p}(gl_{
 1\,tor})$ and Jordan quiver gauge theories
DTSTART:20230912T083000Z
DTEND:20230912T093000Z
DTSTAMP:20260522T144600Z
UID:indico-event-10087@indico.math.cnrs.fr
DESCRIPTION:After reviewing the elliptic quantum group $U_{q\,p}(g)$ assoc
 iated with the affine Lie algebra $g$\, we introduce a new elliptic quantu
 m toroidal algebra $U_{q\,t\,p}(gl_{1\,tor})$. By using the vertex operato
 rs (the intertwining operators) of the $U_{q\,t\,p}(gl_{1\,tor})$-modules 
 w.r.t. the Drinfeld comultiplication\, we give a realization of the affine
  quiver W-algebra $W_{q\,t}(\\Gamma(\\widehat{A_0}))$ proposed by Kimura
 –Pestun. This realization turns out to be useful to derive the Nekrasov 
 instanton partition functions of the 5d and 6d lifts of the 4d $N = 2^∗$
  theories\, i.e. the generating functions of the $\\chi_y$- and the ellipt
 ic genus of the instanton moduli spaces\, and provide a new Alday–Gaio
 tto–Tachikawa correspondence.\n\nhttps://indico.math.cnrs.fr/event/10087
 /
URL:https://indico.math.cnrs.fr/event/10087/
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