Notes on Macdonald Polynomials and the Geometry of Hilbert Schemes

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Torus knots and the rational DAHA (2012, unknown): “,t]: ϕ1−q : pk → (1− q k)p k, ϕ 1 1−q : pk → 1 1−qk pk; ϕ1−t : pk → (1−t k)p k, ϕ1 1−t : pk → 1 1− tk pk. The following theorem is a deﬁnition of the modiﬁed Macdonald polynomials . Theorem 6.2 (e.g. [Hai02b]). There is a homogeneousQ(q,t)-basis{He µ}of Λwhose elements are uniquely characterized by ”
The local Donaldson–Thomas theory of curves (2005, background): “The exponents in the formula are well known to be the weights of tangent action, see for example Haiman [11].”
The refined topological vertex (2007, background): “The weight at the fixed point labeled by the partition ν is given by [10, 27] ∑”