Speaker
Hitoshi Konno
(Tokyo University of Marine Science and Technology)
Description
We introduce a new elliptic quantum toroidal algebra $U_{q,t,p}(\mathfrak{gl}_{1,tor})$ and show some interesting representations including the level (0,0) representation given by the elliptic Ruijsenaars difference operators. We also construct intertwining operators of the $U_{q,t,p}(\mathfrak{gl}_{1,tor})$-modules w.r.t. the Drinfeld comultiplication and give a realization of the affine quiver W-algebra $W_{q,t}(\Gamma(A_0))$ proposed by Kimura–Pestun. This realization turns out to be useful to derive the Nekrasov instanton partition functions, i.e. the $\chi_y$- and elliptic- genus of the moduli spaces, of the 5d and 6d lifts of the 4d ${\cal N} = 2^∗$ theories and provide a new Alday–Gaiotto–Tachikawa correspondence.
Primary author
Hitoshi Konno
(Tokyo University of Marine Science and Technology)
