Psi-functions, irreducible characters and a conjecture of merris and watkins
Thomas H. Pate · Linear and Multilinear Algebra · 1993
In recent articles P. Heyfron has extensively developed the properties of certain class functions, known as φ-functions, defined on the symmetric groups. The generalized matrix function d φ, associated with φ-function φ, is non-negative when restricted to Hermitian positive semi-definite matrices. Consequently, the φ-functions have proved useful in obtaining matrix inequalities, particularly involving immanants. We present two formulas that express irreducible characters as linear combinations of φ-funtions. Moreover, we obtain inequalities among φ-functions which lead to new inequalities among immanants. We also partially resolve a conjecture of Merris and Watkins.