Row appending maps, Ψ-functions, and immanant inequalities for Hermitian positive semi-definite matrices

Proceedings of the London Mathematical Society

Volumn 76, Issue 2, 1998, Pages 307-358

  Pate, Thomas H ^a  

^a AUBURN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002132064     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611598000100     Document Type: Article

References (35)

1. I. P. GOULDEN and D. M. JACKSON, 'Immanants of combinatorial matrices', J. Algebra 148 (1992) 305-324.
2. R. GRONE and S. PIERCE, 'Permanental inequalities for correlation matrices', SIAM J. Matrix Anal. Appl. 9 (1988) 194-201.
3. M. HAIMAN, 'Hecke algebra characters and immanant conjectures', J. Amer. Math. Soc. 6 (1993) 569-595.
4. P. HEYFRON, 'Positive functions defined on Hermitian positive semi-definite matrices', Ph.D. thesis. Imperial College, London. 1989.
5. P. HEYFRON, 'Immanant dominance orderings for hook partitions', Linear and Multilinear Algebra 24 (1988) 65-78.
6. P. HEYFRON, 'Some inequalities concerning immanants', Math. Proc. Cambridge Philos. Soc. 109 (1991) 15-30.
7. G. D. JAMES, 'Hecke algebras and immanants', Linear Algebra Appl. 197/198 (1994) 659-670.
8. G. D. JAMES and A. KERBER, The representation theory of the symmetric group, Encyclopedia of Mathematics 16 (Addison-Wesley, Reading, Mass., 1981).
9. G. D. JAMES and M. W. LIEBECK, 'Permanents and immanants of Hermitian matrices', Proc. London Math. Soc. (3) 55 (1987) 243-265.
10. G. JAMES, C. JOHNSON, and S. PIERCE, 'Generalized matrix function inequalities on M-matrices', preprint, Imperial College, London, 1996.
11. E. H. LIEB, 'Proofs of some conjectures on permanents', J. Math. Mech. 16 (1966) 127-134.
12. M. MARCUS, 'The Hadamard theorem for permanents', Proc. Amer. Math. Soc. 15 (1964) 967-973.
13. R. MERRIS, 'The permanental dominance conjecture', Current trends in matrix theory (eds R. Grone and F. Uhlig, Elsevier, New York, 1987), pp. 213-223.
14. R. MERRIS and W. WATKINS, 'Inequalities and identities for generalized matrix functions', Linear Algebra Appl. 64 (1985) 223-242.
15. R. GRONE and R. MERRIS, 'Conjectures on permanents', Linear and Multilinear Algebra 21 (1987) 419-427.
16. H. MINC, Permanents, Encyclopedia of Mathematics 6 (Addison-Wesley, Reading, Mass., 1978).
17. M. A. NAIMARK and A. I. STERN, Theory of group representations. Grundlehren der Mathematischen Wissenschaften 246 (Springer, Berlin, 1982).
18. T. H. PATE, 'Inequalities relating groups of diagonal products in a Gram matrix', Linear and Multilinear Algebra 11 (1982) 1-17.
19. T. H. PATE, 'Lower bounds for permanents of Gram matrices having a rank one principal submatrix', Linear Algebra Appl. 111 (1988) 249-259.
20. T. H. PATE, 'Permanental dominance and the Soules conjecture for certain right ideals in the group algebra', Linear and Multilinear Algebra 24 (1989) 135-149.
21. T. H. PATE, 'Partitions, irreducible characters, and inequalities for generalized matrix functions', Trans. Amer. Math. Soc. 325 (1991) 875-894.
22. T. H. PATE, 'Immanant inequalities and partition node diagrams', J. London Math. Soc. (2) 46 (1992) 65-80.
23. T. H. PATE, 'Tensor products, symmetric products, and permanents of positive semi-definite Hermitian matrices', Linear and Multilinear Algebra 31 (1992) 27-36.
24. T. H. PATE, 'Descending chains of immanants', Linear Algebra Appl. 162/164 (1992) 639-650.
25. T. H. PATE, 'Psi-functions, permutations characters, and a conjecture of Merris and Watkins', Linear and Multilinear Algebra 35 (1993) 195-212.
26. T. H. PATE, 'Immanant inequalities, induced characters, and rank two partitions', J. London Math. Soc. (2) 49 (1994) 40-60.
27. T. H. PATE, 'Inequalities involving immanants', Linear Algebra Appl. 212/213 (1994) 31-44.
28. T. H. PATE. 'Group algebras, monotonicity, and the Lieb permanent inequality', Linear and Multilinear Algebra 40 (1996) 207-220.
29. T. H. PATE, 'Exterior products, elementary symmetric functions, and the Fischer determinant inequality', Linear Algebra Appl. 255 (1997) 203-242.
30. J. RIORDAN, Combinatorial identities (John Wiley, New York. 1968).
31. J. STEMBRIDGE, 'Some conjectures for immanants', Canad. J. Math. 44 (1992) 1079-1099.
32. J. STEMBRIDGE, 'Immanants of totally positive matrices are non-negative', Bull. London Math. Soc. 23 (1991) 422-128.
33. R. STANLEY and J. STEMBRIDGE, 'On immanants of Jacobi-Trudi matrices and permutations with restricted position', J. Combin. Theory Ser. A 62 (1993) 263-279.
34. I. SCHUR, 'Über endlicher Gruppen und Hermiteschen Formen', Math. Z. 1 (1918) 184-207.
35. m defined by generalized matrix functions', Linear Algebra Appl. 257 (1997) 193-200.