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I. Schur (1918)
Über endliche Gruppen und Hermitesche FormenMathematische Zeitschrift, 1
I. Goulden, D. Jackson (1992)
Immanants of combinatorial matricesJournal of Algebra, 148
C. Cryer (1976)
Some properties of totally positive matricesLinear Algebra and its Applications, 15
(1968)
Total positivity (Stanford
S. Karlin, Y. Rinott (1988)
A generalized Cauchy-Binet formula and applications to total positivity and majorizationJournal of Multivariate Analysis, 27
C. Greene (1992)
Proof of a conjecture on immanants of the Jacobi-Trudi matrixLinear Algebra and its Applications, 171
(1918)
Math. Z
Immanant conjectures and Kazhdan-Lusztig polynomials', preprint
安藤 毅 (1984)
Totally positive matrices
J. Stembridge (1992)
Some Conjectures for ImmanantsCanadian Journal of Mathematics, 44
G. Oliveira (1973)
Generalized matrix functions
IMMANANTS OF TOTALLY POSITIVE MATRICES ARE NONNEGATIVE JOHN R. STEMBRIDGE Introduction Let M {k) denote the algebra of n x n matrices over some field k of characteristic zero. For each A>valued function / on the symmetric group S , we may define a corresponding matrix function on M (k) in which w a (fljji— • > X\ )&i (i)'" ( )' (U weS If / is an irreducible character of S , these functions are known as immanants; if/ is an irreducible character of some subgroup G of S (extended trivially to all of S by n n defining /(vv) = 0 for w$G), these are known as generalized matrix functions. Note that the determinant and permanent are obtained by choosing / to be the sign character and trivial character of S , respectively. We should point out that it is more traditional to use /(vv) in (1) where we have used /(W ) . This change can be undone by transposing the matrix. If/ happens to be -1 a character, then /(w ) = x(w), so the generalized matrix function we have indexed by / is the complex conjugate of the traditional one. Since the characters of
Bulletin of the London Mathematical Society – Wiley
Published: Sep 1, 1991
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