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Pré-Publication, Document De Travail Année : 2010

New induction relations for complete functions in Jucys-Murphy elements

Résumé

The problem of computing the class expansion of some symmetric functions evaluated in Jucys-Murphy elements appears in different contexts, for instance in the computation of matrix integrals. Recently, M. Lassalle gave a unified algebraic method to obtain some induction relations on the coefficients in this kind of expansion. In this paper, we give a simple purely combinatorial proof of his result. Besides, using the same type of argument, we obtain new simpler formulas. We also prove an analogous formula in the Hecke algebra of $(S_{2n},H_n)$ and use it to solve a conjecture of S. Matsumoto on the subleading term of orthogonal Weingarten function. Finally, we propose a conjecture for a continuous interpolation between both problems.
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Dates et versions

hal-00512865 , version 1 (31-08-2010)
hal-00512865 , version 2 (22-03-2011)
hal-00512865 , version 3 (01-06-2011)

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Citer

Valentin Féray. New induction relations for complete functions in Jucys-Murphy elements. 2010. ⟨hal-00512865v2⟩
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