Results 1 to 10 of about 333 (95)
Jack polynomials and affine Yangian
Nuclear Physics B, 2022 In this paper, we define one kind of new Jack polynomials denoted by Jkλ, which equal the standard Jack polynomials Pλα multiplied by a coefficient. We show that the structure constant Cλμν in Jkλ⋅Jkμ=∑νCλμνJkν can be given from affine Yangian of gl(1 ...
Zhennan Cui, Yang Bai, Na Wang, Ke Wu
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Cumulants of Jack symmetric functions and b-conjecture (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series ψ(x, y, z; t, 1 + β) that might be interpreted as a continuous deformation of the rooted hypermap generating series.
Maciej Dolega, Valentin Féray
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3D bosons, 3-Jack polynomials and affine Yangian of gl 1 $$ \mathfrak{gl}(1) $$
Journal of High Energy Physics, 2023 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.
Na Wang, Ke Wu
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On Kerov polynomials for Jack characters (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We give a partial
Valentin Féray, Maciej Dołęga
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From superintegrability to tridiagonal representation of β-ensembles
Physics Letters B, 2022 The wonderful formulas by I. Dumitriu and A. Edelman [1,2] rewrite β-ensemble, with eigenvalue integrals containing Vandermonde factors in the power 2β, through integrals over tridiagonal matrices, where β-dependent are the powers of individual matrix ...
A. Mironov, A. Morozov, A. Popolitov
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Dual combinatorics of zonal polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In this paper we establish a new combinatorial formula for zonal polynomials in terms of power-sums. The proof relies on the sign-reversing involution principle.
Valentin Féray, Piotr Sniady
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Quantum Hall ground states and regular graphs
Nuclear Physics B, 2022 We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop a graph-based ansatz to construct trial FHQ ground states sharing the local properties of Jack polynomials.
Hamed Pakatchi
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European Physical Journal C: Particles and Fields, 2022 We construct the ( $$\beta $$ β -deformed) partition function hierarchies with W-representations. Based on the W-representations, we analyze the superintegrability property and derive their character expansions with respect to the Schur functions and ...
Rui Wang +3 more
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CFT approach to constraint operators for (β-deformed) hermitian one-matrix models
Nuclear Physics B, 2022 Since the (β-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the constraints can be ...
Rui Wang +3 more
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Journal of High Energy Physics, 2023 In this paper, we consider 3D Young diagrams with at most N layers in z-axis direction, which can be constructed by N 2D Young diagrams on slice z = j, j = 1, 2, · · · , N from the Yang-Baxter equation.
Na Wang, Ke Wu
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