Results 1 to 10 of about 95 (87)
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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Vector-Valued Jack Polynomials from Scratch [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 Vector-valued Jack polynomials associated to the symmetric group S_N are polynomials with multiplicities in an irreducible module of S_N and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning
Jean-Gabriel Luque, Charles F. Dunkl
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Some Singular Vector-Valued Jack and Macdonald Polynomials [PDF]
Symmetry, 2019 For each partition τ of N, there are irreducible modules of the symmetric groups S N and of the corresponding Hecke algebra H N t whose bases consist of the reverse standard Young tableaux of shape τ . There are associated spaces of nonsymmetric Jack and Macdonald polynomials taking values in these modules.
Charles Dunkl
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A recursion and a combinatorial formula for Jack polynomials
Inventiones Mathematicae, 1997 Preprint March 1996, to appear in Invent.
Friedrich Knop, Siddhartha Sahi
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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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Jack Polynomials in Superspace [PDF]
Communications in Mathematical Physics, 2003 This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric ...
Desrosiers, P. +2 more
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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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Determinantal Expression and Recursion for Jack Polynomials [PDF]
The Electronic Journal of Combinatorics, 1999 We describe matrices whose determinants are the Jack polynomials expanded in terms of the monomial basis. The top row of such a matrix is a list of monomial functions, the entries of the sub-diagonal are of the form $-(r\alpha+s)$, with $r$ and $s \in {\bf N^+}$, the entries above the sub-diagonal are non-negative integers, and below all entries are ...
Lapointe, L., Lascoux, Alain, Morse, J.
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A superpolynomial version of nonsymmetric Jack polynomials [PDF]
The Ramanujan Journal, 2021 Superpolynomials consist of commuting and anti-commuting variables. By considering the anti-commuting variables as a module of the symmetric group the theory of vector-valued nonsymmetric Jack polynomials can be specialized to superpolynomials. The theory significantly differs from the supersymmetric Jack polynomials introduced and studied in several ...
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