- Structure coefficients of the hecke algebra of (s2n,bn), Electronic Journal of Combinatorics 21(4) (2014), \#P4.35

Abstract: In this paper, we give a polynomiality property for the structure coefficients of the Hecke algebra of (S_{2n}, B_n). Our main tool is a combinatorial algebra which projects onto the Hecke algebra of (S_{2n},\mathcal{B}_n) for every n. To build it, we use partial bijections and we introduce and study a new class of finite dimensional algebras. We show also that a particular sub-algebra of it is isomorphic to the algebra of 2-shifted symmetric functions. We are able to give upper-bounds to the degree of the polynomials of the structure coefficients.

- Structure coefficients of the hecke algebra of (s2n,bn) . DMTCS Proceedings, 0(01), 2013.

Abstract: This is an extended abstract of the paper above which focuses on the polynomiality property for the structure coefficients of the Hecke algebra of (S_{2n}, B_n).

- Polynomialité des coefficients de structure des algèbres de doubles-classes, in preparation.

Abstract: We study in this paper the dependence on n of the structure coefficients in the case of a sequence of double-class algebras. We give a general framework which contains both polynomiality properties of the center of the symmetric group algebra and of the double-class algebra of the pair (S_{2n},B_n). In addition, we show that this general framework implies a polynomiality property for the structure coefficients of other interesting algebras.

- A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs, unpublished notes.

Abstract: We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to a "Frobenius formula" for Gelfand pairs. For a given Gelfand pair, the structure coefficients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalisation of the Frobenius formula which writes the structure coefficients of the center of a finite group algebra in terms of irreducible characters.

- Polynomialité des coefficients de structure des algèbres de doubles-classes, thèse de doctorat, Université de Bordeaux, 2014.

Abstract: This is my PHD thesis manuscript. It contains with details all the results of the previous papers and more. It is written in French but there is a "State of art" section and "Abstract" one written in English for non-French speaking researchers.