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| XXXIX Workshop on Geometric Methods in Physics | 19.06–25.06.2022 |
| XI School on Geometry and Physics | 27.06–1.07.2022 |
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Hitoshi KonnoElliptic Quantum Toroidal Algebra $U_{q,t,p}(gl_{1,tor})$ and affine quiver gauge theoriesWe introduce the elliptic quantum toroidal algebra $U_{q,t,p}(gl_{1,tor})$. After giving some representations including the level (0,0) representation realized by using the elliptic Ruijsenaars difference operator, we construct intertwining operators of the $U_{q,t,p}(gl_{1,tor})$-modules w.r.t. the Drinfeld comultiplication. We then show that $U_{q,t,p}(gl_{1,tor})$ gives 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, i.e. the $\chi_y$- and elliptic genus, of the 5d and 6d lifts of the 4d ${\cal N}=2^*$ theories and provide a new Alday-Gaiotto-Tachikawa correspondence. |
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| University of Bialystok |
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