A machine for producing inequalities involving immanants and other generalized matrix functions

Abstract

There are many known inequalities involving the restriction of immanants and other generalized matrix functions to the set of positive semidefinite Hermitian matrices. We present a general scheme for obtaining such inequalities. Matrix theoretic refinements of Lieb's and Fischer's inequalities, recently discovered by Pate, are obtainable using the scheme. Other known inequalities are discussed, and we derive new inequalities that relate characters constructed from generalized diagrams.