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

Yusuke Ohkubo, Hidetoshi Awata, Hiroki Fujino

Published 2015-12-25Version 1

In this paper, we consider the $q \rightarrow 0$ 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, we obtain a formula for the 4-point correlation function of a certain operator.