Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence

Abstract

In this paper, we consider the $q\to 0$ limit of the deformed Virasoro algebra and that of the level 1, 2 representation of Ding-Iohara-Miki algebra. Moreover, 5D AGT correspondence at this limit is discussed. This specialization corresponds to the limit from Macdonalds functions to Hall-Littlewood functions. Using the theory of Hall-Littlewood functions, some problems are solved. For example, the simplest case of 5D AGT conjectures is proven at this limit, and we obtain a formula for the 4-point correlation function of a certain operator.

arXiv comment32 pages, 1 figure

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Cited by in corpus (18)

• 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
• A slow review of the AGT correspondence
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• q-Painleve equation from Virasoro constraints
• ABCD of qq-characters
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• On generalized Macdonald polynomials
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Shifted quantum groups and matter multiplets in supersymmetric gauge theories
• Engineering 3D $\mathcal{N}=2$ theories using the quantum affine $\mathfrak{sl}(2)$ algebra
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins