A few remarks on colour–flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals

摘要: We investigate diverse relations of the colour–flavour transformations (CFT) introduced by Zirnbauer in 'Supersymmetry for systems with unitary disorder: circular ensembles' (1996 J. Phys. A: Math. Gen. 29 7113–36) to various topics random matrix theory and multivariate analysis, such as measures on truncations matrices, Jacobi ensembles Berezin reproducing kernels a generalization Selberg integral due Kaneko, Kadell Yan involving Schur functions. Apart from suggesting explicit formulae bosonic CFT group range parameters beyond that Zirnbauer's paper we also suggest an alternative variant transformation integration going over unbounded domain pair Hermitian matrices. The latter makes possible evaluation certain averages theory.