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arXiv · 2212.05665

3D Bosons, 3-Jack polynomials and affine Yangian of ${\mathfrak{gl}}(1)$

Na Wang·Ke Wu
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Abstract

3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters $h_1,h_2,h_3$ to $y,x,z$-axis respectively. 3-Jack polynomials are polynomials of $P_{n,j}, n\geq j$ with coefficients in $\mathbb C(h_1,h_2,h_3)$, which are the generalization of Schur functions and Jack polynomials to 3D case. Similar to Schur functions, 3-Jack polynomials can also be determined by the vertex operators and the Pieri formulas.

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Na Wang, Ke Wu. 2022-12-12. 3D Bosons, 3-Jack polynomials and affine Yangian of ${\mathfrak{gl}}(1)$. https://doi.org/10.1007/jhep03(2023)232

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