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We study symmetric polynomials whose variables are odd-numbered Jucys-Murphy elements.
A. Jucys, Symmetric polynomials and the center of the symmetric group ring , Reports on Mathematical Physics 5
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I. G. Macdonald, Symmetric Functions and Hall Polynomials , second ed., Oxford University Press, Oxford, 1995
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A. Okounkov and G. Olshanski, shifted Jack polynomials, binomial formula, and applications , Math. Research Lett. 4
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S. Kerov, A. Okounkov, and G. Olshanski, The boundary of the Young graph with Jack edge multiplicities , Internat. Math. Res. Notices (1998), no. 4, 173–199
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M. Lassalle, Some combinatorial conjectures for Jack polynomials , Ann. Comb. 2
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B. E. Sagan, The symmetric group. Representations, combinatorial algorithms, and symmetric functions , second ed., Graduate Texts in Mathematics, 203
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B. Collins, Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability , Int. Math. Res. Not. 2003, no. 17, 953–982
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A. Lascoux and J.-Y. Thibon, Vertex operators and the class algebras of symmetric groups , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 283
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M. Lassalle, Jack polynomials and some identities for partitions , Trans. Amer. Math. Soc. 356
2004
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A. Borodin and G. Olshanski, Z-measures on partitions and their scaling limits , European J. Combin. 26
2005
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B. Collins and P. Śniady, Integration with respect to the Haar measure on unitary, orthogonal and symplectic group , Commun. Math. Phys. 264
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M. Lassalle, A positivity conjecture for Jack polynomials , Math. Res. Lett. 15
2008
Later among the works it cites.
S. Matsumoto, Jack deformations of Plancherel measures and traceless Gaussian random matrices , Electr. J. Combin. 15
2008
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B. Collins and S. Matsumoto, On some properties of orthogonal Weingarten functions , J. Math. Phys. 50
2009
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M. Lassalle, Jack polynomials and free cumulants , Advances in Mathematics 222
2009
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J. Novak, Jucys-Murphy elements and Weingarten function , Banach Center Publ. 89
2010
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G. Olshanski, Plancherel averages: remarks on a paper by Stanley , Electr. J. Combin. 17
2010
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S.-E. Cheng, S.-P. Eu, and T.-S. Fu, Area of Catalan paths on a checkerboard , European J. Combin. 28
2007
Cited alongside, same era.
S. Fujii, H. Kanno, S. Moriyama, and S. Okada, Instanton calculus and chiral one-point functions in supersymmetric gauge theories , Adv. Theor. Math. Phys. 12
2008
Cited alongside, same era.
A. Garsia, Young’s seminormal representation and Murphy elements and content evaluations , Lecture Notes in Algebraic Combinatorics, available at: http://math.ucsd.edu/~garsia/
Cited in the paper.
M. Lassalle, available at http://igm.univ-mlv.fr/~lassalle/jack.html
Cited in the paper.
S. Matsumoto and J. Novak, Jucys-Murphy elements and unitary matrix integrals , arXiv:0905.1992v2
Cited in the paper.
Cited in the paper.
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P. Zinn-Justin, Jucys-Murphy elements and Weingarten matrices , Lett. Math. Phys. 91
2010
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