List of publications
characters of the
Jack polynomials :
A conjecture for
and free cumulants
Research interests :
- Mathematical physics
Properties of n-point functions in general quantum field
Exactly solvable quantum many-body systems (Calogero-Sutherland type).
- Groups and complex analysis
Harmonic analysis in complex homogeneous spaces :
Generalized Reinhardt domains, Hardy spaces, Cauchy and Poisson kernels.
Generalization of the tube and three-circle theorems.
- Hermitian symmetric spaces
Orbital structure, harmonic analysis, Hua equations, R-spaces.
- Jordan algebras
Formally real and complex Jordan algebras :
Inversible elements, Pierce decomposition.
Quasi-invariant measures on the cone of squares.
- Algebraic combinatorics
Symmetric functions, classical theory of partitions.
Jack polynomials, Macdonald polynomials.
Generalization of classical orthogonal polynomials (Hermite, Laguerre, Jacobi).
Generalized binomial coefficients.
Shifted Jack polynomials, shifted Macdonald polynomials.
Characters of the symmetric group.
- Free probability theory