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

Journal of Mathematical Physics. 2017. Vol. 58. No. 071704. P. 1-26.
Окубо Ю., Awata H., Fujino H.

In this paper, we consider the q → 0 limit of the deformed Virasoro algebra and that of the level 1, 2 representation of the Ding-Iohara-Miki algebra. Moreover, 5D AGT correspondence in 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 in this limit, and we obtain a formula for the 4-point correlation function of a certain operator.