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

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 $P_{n,j},n\ge j$ 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.

References in corpus (1)

• Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations

Cited by in corpus (1)

• Quantum toroidal algebras and solvable structures in gauge/string theory