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

2015/12/25 by Ohkubo, Yusuke, Awata, Hidetoshi, Fujino, Hiroki
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1512.08016

Abstract

In this paper, we consider the q → 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.

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