Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
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Abstract We show that the wreath Macdonald polynomials for$$\mathbb {Z}/\ell \mathbb {Z}\wr \Sigma _n$$ , when naturally viewed as elements in the vertex representation of the quantum toroidal algebra$$U_{\mathfrak {q},\mathfrak {d}}(\ddot{\mathfrak {sl}}_\ell )$$ , diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials.more » « less
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