Symmetric Functions and 3D Fermion Representation of $$\pmb {W_{1+\infty }}$$ Algebra

Wang, Na; Yang, Bai; Zhennan, Cui; Wu, Ke

doi:10.1007/s00006-022-01247-7

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…For j = 1, 2, • • • , N , the Boson algebra a j,n has an representation on 2D Young diagrams λ or the symmetric functions Y λ , where Y λ are defined in [18] and are functions of power sums p n , n = 1, 2, • • • . The symmetric functions Y λ become 2D Jack polynomials when…”

Section: The Littlewood-richardson Rule For 3-jack Polynomialsmentioning

confidence: 99%

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3D Bosons and W1+∞ algebra

Wang

2023

J. High Energ. Phys.

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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. Using 2D Bosons {aj,m, m ∈ ℤ} associated to 2D Young diagrams on the slice z = j, we constructed 3D Bosons. Then we show the 3D Boson representation of W1+∞ algebra, and give the method to calculate the Littlewood-Richardson rule for 3-Jack polynomials.

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Section: The Littlewood-richardson Rule For 3-jack Polynomialsmentioning

confidence: 99%

“…Since we have known the representation of affine Yangian of gl(1) on 3D Young diagrams, in the following, we use the generators of affine Yangian of gl(1) to represent 3D Bosons. We know that [18]…”

Section: Jhep05(2023)174 6 the Representation Of 3d Bosons On 3d Youn...mentioning

confidence: 99%

3D Bosons and W1+∞ algebra

Wang

2023

J. High Energ. Phys.

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“…In [11], 3-Jack polynomials are obtained under the condition ψ 0 = 1 which does not lose the generality. In fact, if we calculate the 3-Jack polynomials for general ψ 0 , the 3-Jack polynomials will become the symmetric functions Y λ when ψ 0 = − 1 h 1 h 2 , where Y λ are defined by us in [19,20]. Therefore, 3-Jack polynomials are the generalization of the symmetric functions Y λ to 3D Young diagrams,…”

Section: Jhep03(2023)232mentioning

confidence: 99%

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

Wang

2023

J. High Energ. Phys.

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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 h1, h2, h3 to y, x, z-axis respectively. 3-Jack polynomials are polynomials of Pn,j, n ≥ j with coefficients in ℂ(h1, h2, h3), 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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“…From [18], we know that the operators of the affine Yangian of gl( 1) can be represented by a series of 2D Bosons a j,n :…”

Section: D Boson Representation Of Affine Yangian Of Gl(1)mentioning

confidence: 99%

School Mathematics Textbooks in China

Wang¹

2015

East China Normal University Scientific Reports

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Let µ and ν be two probability measures on R d , where µ(dx) = e −V (x) dx R d e −V (x) dx for some V ∈ C 1 (R d ). Explicit sufficient conditions on V and ν are presented such that µ * ν satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, if V (x) = λ|x| 2 for some λ > 0 and ν(e λθ|•| 2 ) < ∞ for some θ > 1, then µ * ν satisfies the log-Sobolev inequality. This improves and extends the recent results on the log-Sobolev inequality derived in [20] for convolutions of the Gaussian measure and compactly supported probability measures. On the other hand, it is well known that the log-Sobolev inequality for µ * ν implies ν(e ε|•| 2 ) < ∞ for some ε > 0. RésuméDes conditions explicites suffisantes sur V et ν sont présentées telles que µ * ν satisfait des inégalités de Sobolev logarithmique, de Poincaré et de super-Poincaré. En particulier, si V (x) = λ|x| 2 pour quelque λ > 0 et ν(e λθ|•| 2 ) < ∞ avec θ > 1, alors µ * ν satisfait l'inégalité de Sobolev logarithmique. Cela améliore et étend des résultats récents sur l'inégalité de Sobolev logarithmique obtenus dans [20] pour des convolutions de la mesure de Gauss et des mesures de probabilité à support compact. D'autre part, il est bien connu que l'inégalité de Sobolev logarithmique pour µ * ν implique ν(e ε|•| 2 ) < ∞ pour quelque ε > 0.

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Symmetric Functions and 3D Fermion Representation of $$\pmb {W_{1+\infty }}$$ Algebra

Cited by 7 publications

References 19 publications

3D Bosons and W1+∞ algebra

3D Bosons and W1+∞ algebra

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

School Mathematics Textbooks in China

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