Totally Nonnegative and Oscillatory Elements in Semisimple Groups

  title={Totally Nonnegative and Oscillatory Elements in Semisimple Groups},
  author={Andrei Zelevinsky},
We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F. R. Gantmacher, M. G. Krein, A. Whitney, C. Loewner, M. Gasca, and J. M. Peña to the case of an arbitrary complex semisimple Lie group. 

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Showing 1-9 of 9 references

Total positivity in reductive groups

G. Lusztig
in: Lie theory and geometry: in honor of Bertram Kostant, Progress in Mathematics 123, Birkhäuser • 1994
View 8 Excerpts
Highly Influenced


F. R. Gantmacher, M. G. Krein
Oszillationskerne und Kleine Schwingungen Mechanischer Systeme, Akademie-Verlag, Berlin, 1960. • 1950
View 4 Excerpts
Highly Influenced

Total positivity and Neville elimination

M. Gasca, J. M. Peña
Linear Algebra Appl. 165 • 1992
View 1 Excerpt


K. S. Brown
Springer-Verlag, New York-Berlin • 1989

The theory of matrices

F. R. Gantmacher
Chelsea Pub. Co., 1960. • 1988

Groupes et algèbres de Lie

N. Bourbaki
Ch. IV-VI, Hermann, Paris • 1968
View 1 Excerpt

Total positivity

S. Karlin
Stanford University Press • 1968
View 1 Excerpt

A reduction theorem for totally positive matrices

A. M. Whitney
J. d’Analyse Math. 2 • 1952
View 1 Excerpt

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