On the equality of generalized matrix functions

چکیده مقاله

Let H and K be arbitrary subgroups of the symmetric group Sn and let φ and ψ be irreducible characters of H and K, respectively. The main result of this paper is that the two generalized matrix functions dφH and dψK are equal on the set of singular matrices if and only if φ_H∩K=ψ_H∩K and both of φ and ψ vanish outside of H∩K.