Instanton counting on blowup, I

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Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial (2010, methodology): “Next we recall the Nekrasov partition function (see [15] and [4, 5], [16], [17]).”
The affine Yangian of gl1 revisited (2014, unknown): “Our computations are based on the following well-known result (see [13,16]): Proposition 3.”
REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS (2008, background): “On the string theory side, the topological vertex Cλ1λ2λ3(q) is constructed based on the geometric transition, which is a duality of topological closed string to the Chern-Simons theory [2, 3].”
Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “The explicit form of zvector,hyper[~ Y ] was determined in [3, 18, 19, 20] and given, for instance, in appendix B to [2].”
Matrix models, geometric engineering and elliptic genera (2003, methodology): “The link between the topological string computations and the 5d gauge theory computation of Nekrasov has been proven in [71,72].”