New induction relations for homogeneous functions in Jucys-Murphy elements

Valentin Féray (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The problem of computing the class expansion of some symmetric function 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 its result. Using the same type of argument, we also obtain new simpler formulas. We also prove an analogous formula in the double class algebra and use it to prove a conjecture of S. Matsumoto on the subleading term of orthogonal Weingarten function. Finally, we formulate a conjecture for a continuous interpolation between the two problems.

Mots clés: Jucys-Murphy elements; symmetric group algebra; double coset algebra

Domaines: Combinatoire [math.CO]

Valentin Féray. New induction relations for homogeneous functions in Jucys-Murphy elements. 2010. ⟨hal-00512865v1⟩