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We translate inequalities and conjectures for immanants and generalized matrix functions into inequalities in the L\"owner order.
Marvin Marcus and Henryk Minc, Generalized matrix functions , Trans. Amer. Math. Soc. 116
1965
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John S. Lew, The generalized Cayley-Hamilton theorem in n n dimensions , J. App. Math. Phys. 17
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Robert Grone, Russel Merris, and William Watkins, Cones in the group algebra related to Schur’s determinantal inequality , Rocky Mountain J. Math. 18
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R. Merris, Multilinear Algebra , CRC Press, 1997
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Gi-Sang Cheon and Ian M. Wanless, An update on Minc’s survey of open problems involving permanents , Linear Algebra Appl. 403
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Bertram Kostant, A Theorem of Frobenius, a Theorem of Amitsur-Levitski and Cohomology Theory , pp. 64–91, Springer New York, New York, NY, 2009
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Peter Webb, A course in finite group representation theory , Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2016
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Fuzhen Zhang, An update on a few permanent conjectures , Spec. Matrices 4
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Hans Maassen and Burkhard Kümmerer, Entanglement of symmetric Werner states , available online at http://www.bjadres.nl/MathQuantWorkshop/Slides/SymmWernerHandout.pdf , May 2019
2019
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Felix Huber, Positive maps and trace polynomials from the symmetric group , J. Math. Phys. 62
2021
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