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Tensor inequalities, \(\xi\)-functions and inequalities involving immanants. (English) Zbl 0935.15019

This paper improves the result of the author’s recent paper [Proc. Lond. Math. Soc., III. Ser. 76, No. 2, 307-358 (1998; Zbl 0907.15011)]. Using the same notations as in that paper, he shows that permanent dominance holds for all immanants whose associated partitions are of the form \((p,q^2,r)\).
Inequalities involving immanants have often been obtained using a \(\Psi\)-function. The results on immanants are obtained by analyzing the \(\xi\)-functions, that are more fundamental than the \(\Psi\)-functions. The \(\xi\)-functions arise from a study of tensor constructions and a special collection of quadratic forms defined on spaces of bi-symmetric tensors.
Reviewer: Y.Kuo (Knoxville)

MSC:

15A45 Miscellaneous inequalities involving matrices
15A63 Quadratic and bilinear forms, inner products
15A15 Determinants, permanents, traces, other special matrix functions
15A72 Vector and tensor algebra, theory of invariants

Citations:

Zbl 0907.15011
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