La mesure de Plancherel décalée est une mesure de probabilité naturelle sur les partitions strictes. Nous démontrons une propriété de polynomialité pour les moyennes de mesures de Plancherel décalées. Comme application, nous donnons une nouvelle preuve de certaines formules d’évaluation des contenus obtenues par Han et Xiong très récemment. Nous utilisons, comme outil principal, les -fonctions de Schur factorielles.
The shifted Plancherel measure is a natural probability measure on strict partitions. We prove a polynomiality property for the averages of the shifted Plancherel measure. As an application, we give alternative proofs of some content evaluation formulas, obtained by Han and Xiong very recently. Our main tool is factorial Schur -functions.
Keywords: strict partition, Plancherel measure, Schur $Q$-function, content
Mots clés : partitions strictes, mesure de Plancherel, $Q$-fonction de Schur, contenu
@article{AMBP_2017__24_1_55_0,
author = {Matsumoto, Sho},
title = {Polynomiality of shifted {Plancherel} averages and content evaluations},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {55--82},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {24},
number = {1},
year = {2017},
doi = {10.5802/ambp.364},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.364/}
}
TY - JOUR AU - Matsumoto, Sho TI - Polynomiality of shifted Plancherel averages and content evaluations JO - Annales mathématiques Blaise Pascal PY - 2017 SP - 55 EP - 82 VL - 24 IS - 1 PB - Annales mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.364/ DO - 10.5802/ambp.364 LA - en ID - AMBP_2017__24_1_55_0 ER -
%0 Journal Article %A Matsumoto, Sho %T Polynomiality of shifted Plancherel averages and content evaluations %J Annales mathématiques Blaise Pascal %D 2017 %P 55-82 %V 24 %N 1 %I Annales mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.364/ %R 10.5802/ambp.364 %G en %F AMBP_2017__24_1_55_0
Matsumoto, Sho. Polynomiality of shifted Plancherel averages and content evaluations. Annales mathématiques Blaise Pascal, Tome 24 (2017) no. 1, pp. 55-82. doi : 10.5802/ambp.364. http://www.numdam.org/articles/10.5802/ambp.364/
[1] Multiplicative central measures on the Schur graph, J. Math. Sci., Volume 96 (1999) no. 5, pp. 3472-3477 | DOI | Zbl
[2] Content evaluation and class symmetric functions, Adv. Math., Volume 188 (2004) no. 2, pp. 315-336 | DOI | Zbl
[3] Gaussian fluctuations of Young diagrams and structure constants of Jack characters, Duke Math. J., Volume 165 (2016) no. 7, pp. 1193-1282 | Zbl
[4] Stanley’s formula for characters of the symmetric group, Ann. Comb., Volume 13 (2010) no. 4, pp. 453-461 | DOI | Zbl
[5] On complete functions in Jucys–Murphy elements, Ann. Comb., Volume 16 (2012) no. 4, pp. 677-707 | DOI | Zbl
[6] Instanton calculus and chiral one-point functions in supersymmetric gauge theories, Adv. Theor. Math. Phys., Volume 12 (2008) no. 6, pp. 1401-1428 | DOI | Zbl
[7] Some conjectures and open problems on partition hook lengths, Exp. Math., Volume 18 (2009) no. 1, pp. 97-106 | DOI | Zbl
[8] New hook-content formulas for strict partitions, DMTCS proc. BC (FPSAC 2016) (2016), pp. 635-646
[9] Projective Representations of the Symmetric Groups. Q-Functions and Shifted Tableaux, Oxford Mathematical monographs, Clarendon Press, 1992, xiii+304 pages | Zbl
[10] Dimensions of skew-shifted Young diagrams and projective characters of the infinite symmetric group, J. Math. Sci., Volume 96 (1999) no. 5, pp. 3517-3530 | DOI | Zbl
[11] Interpolation analogues of Schur -functions, J. Math. Sci., Volume 131 (2005) no. 2, pp. 5495-5507 | DOI | Zbl
[12] The algebra of conjugacy classes in symmetric groups and partial permutations, J. Math. Sci., Volume 107 (2001) no. 5, pp. 4212-4230 | DOI | Zbl
[13] Kerov’s central limit theorem for the Plancherel measure on Young diagrams, Symmetric Functions 2001: Surveys of Developments and Perspectives (NATO Sci. Ser. II Math. Phys. Chem.), Volume 74, Kluwer Acad. Publ., Dordrecht (2002), pp. 93-151 | Zbl
[14] Vertex operators and the class algebras of symmetric groups, J. Math. Sci., Volume 121 (2004) no. 3, pp. 2380-2392 | DOI | Zbl
[15] Class expansion of some symmetric functions in Jucys–Murphy elements, J. Algebra, Volume 394 (2013), pp. 397-443 | DOI | Zbl
[16] Symmetric Functions and Hall Polynomials, Clarendon Press, 1995, x+475 pages | Zbl
[17] Correlation functions of the shifted Schur measure, J. Math. Soc. Japan, Volume 57 (2005) no. 3, pp. 619-637 | DOI | Zbl
[18] Jucys–Murphy elements, orthogonal matrix integrals, and Jack measures, Ramanujan J., Volume 26 (2011) no. 1, pp. 69-107 | DOI | Zbl
[19] Jucys–Murphy elements and unitary matrix integrals, Int. Math. Res. Not. (2013) no. 1, pp. 362-397 | DOI | Zbl
[20] Young’s symmetrizers for projective representations of the symmetric group, Adv. Math., Volume 127 (1997) no. 2, pp. 190-257 | DOI | Zbl
[21] Plancherel averages: Remarks on a paper by Stanley, Electron. J. Comb., Volume 17 (2010) no. 1 (#R43, 16 pages) | Zbl
[22] Polynomiality of some hook-length statistics, Ramanujan J., Volume 27 (2012) no. 3, pp. 349-356 | DOI | Zbl
[23] The Howe duality and the projective representations of symmetric groups, Representation Theory, Volume 3 (1999), pp. 416-434 | DOI | Zbl
[24] A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group (2006) (https://arxiv.org/abs/math/0606467)
[25] Some combinatorial properties of hook lengths, contents, and parts of partitions, Ramanujan J., Volume 23 (2010) no. 1-3, pp. 91-105 | DOI | Zbl
[26] The centers of spin symmetric group algebras and Catalan numbers, J. Algebr. Comb., Volume 29 (2009) no. 2, pp. 175-193 | DOI | Zbl
[27] A new approach to the representation theory of the symmetric groups IV. -graded groups and algebras; projective representations of the group , Mosc. Math. J., Volume 8 (2008) no. 4, pp. 813-842 | Zbl
Cité par Sources :
