The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion

Abstract

A root of unity limit of the $q$-deformed Virasoro algebra is considered. The $\widehat{sl}(2{)}_k$ current algebra and the integral formulas of the solutions of the KZ equations can be realized by the $q$-deformed boson at the limit and an additional boson. We explicitly construct the integral representation of the four-point blocks with a $\mathcal{K}$-operator insertion.

15 pages; v2: references added

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Cited by in corpus (10)

• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Anomaly in RTT relation for DIM algebra and network matrix models
• On elementary proof of AGT relations from six dimensions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• Twisted reduction of quiver W-algebras
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Elliptic algebra, Frenkel-Kac construction and root of unity limit